bluuebunny/crossref_metadata_2025 huggingface dataset:
A Two‐Dimensional Computational Droplet Contact Model
Authors: Osman Muhammad , Sauer Roger A.
Published: December 2011

The interaction between capillary fluid films and micro‐structural rough surfaces is one of the main challenges in studying self‐cleaning mechanisms. The surface behavior of the deformable fluid film is governed by the Young‐Laplace equation, which is highly non‐linear. Therefore, a numerical solution is introduced using the finite element method, based on a continuum mechanical formulation. Surface and line contact at the fluid‐structure interface are modeled by enforcing a contact constraint, and a contact angle, respectively. The numerical solution is validated against the analytical solution of a test case. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical study of human dolphin swimming
Authors: Pacholak Steffen , Rudert Alexander , Brücker Christoph
Published: December 2011

Propulsion at human dolphin swimming is gained by performing an undulatory motion through the hole body. This movement is similar to undulatory fish motion. Special physical properties like stiffness of upper and lower extremity parts are creating significant unsteady vortex structures around the hole swimmer when performing dolphin kick. The characteristic of these structures and their influence at propulsion are not very well investigated yet. The present paper discribes the creation of a realistic model using data scans of a female swimmer. It is updated with her unique dolphin motion to simulated complete swim motion. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of the Finite Cell Method to patient‐specific femur simulations
Authors: Ruess Martin , Yosibash Zohar , Trabelsi Nir , Rank Ernst
Published: December 2011

Standard methods for predicting the mechanical response of a human femur bone from quantitative computer‐tomography (qCT) scans are classically based on the h‐version of the finite element method. These methods are often limited in accuracy and efficiency due to the need for segmentation and the slow convergence rate. With the Finite Cell Method (FCM) a high‐order fictitious domain method has been developed that overcomes the aforementioned problems and provides accurate results when compared to high‐order finite element methods and experimental results. Herein the FCM applied to the analysis of a patient‐specific femur is presented. The femur model is determined based on qCT‐scans and the elastic response under compression is presented in terms of strains and displacements. The results are compared with a p‐FE analysis and validated by results from an in‐vitro test of the modeled femur. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A micro‐sphere‐based remodelling formulation for arterial tissue including residual stresses
Authors: Waffenschmidt Tobias , Menzel Andreas
Published: December 2011

An essential property of soft biological tissues is the ability to adapt according to respective loading conditions, e.g. by means of fibre reorientation (remodelling). In particular with regard to arterial tissue, an externally unloaded state of the material is generally associated with residual stresses. In this contribution a three‐dimensional micro‐sphere‐based constitutive model for anisotropic soft biological tissue is presented, which includes fibre‐reorientation‐related remodelling as well as residual stress‐effects. As a key aspect of this contribution, time‐dependent remodelling effects are incorporated by introducing evolution equations for the integration directions of the micro‐sphere scheme, which thereby characterize the material's anisotropic properties. An appropriate remodelling approach for the orthotropic case is discussed, whereas the effect of residual stresses is additionally included in the model by means of a multiplicative decomposition of the deformation gradient tensor. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Passive muscle behaviour – experimental and numerical investigations
Authors: Weichert Christine , Leichsenring Kay , Siebert Tobias , Böl Markus
Published: December 2011

The material behaviour of skeletal muscles can be decomposed into two parts: an active part, describing the contractile mechanisms, and a passive one, characterising the passive components such as the connective tissue. Computational models are used to support the understanding of complex mechanism inside a muscle. In the present work, we focus on the three‐dimensional passive tissue behaviour from the experimental as well as modelling point of view. Therefore, quasi‐static experiments have been performed on specimens with regular geometry. By using a three‐dimensional optical measurement system the shape of the specimens has been reconstructed at different deformation states. On the modelling side a hyperelastic model with transversal isotropic fibre orientation has been used to describe non‐linear stress responses. The model has been validated by performing analyses for different fibre orientations. In summary, it figures out that the proposed modelling approach is able to reflect the experimental results in a satisfying manner. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling and Simulation of Multiple Cracking in Textile Reinforced Concrete Tension Specimen using Fracture Mechanics Approaches
Authors: Azzam Aussama , Richter Mike
Published: December 2011

This paper concerns with the finite element simulation of textile reinforced concrete (TRC) behavior under tension loading by using discrete cracking concept and fracture mechanics approaches. 3D Finite‐Element models are formulated on the meso‐scale by simulating all the heterogeneous structural components, the matrix, the fibers, and the fracture mechanisms in both fiber‐matrix interface, and the discrete cracks of the matrix. The presented numerical simulation in this study allows for better understanding of the stress distribution and the interaction between all damage mechanisms and the corresponding energy dissipations. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A BEM for transient thermoelastic fracture analysis of FGMs
Authors: Ekhlakov Alexander , Khay Oksana , Zhang Chuanzeng , Gao Xiao‐Wei
Published: December 2011

A boundary element method for the transient thermoelastic fracture analysis in isotropic, continuously non‐homogeneous and linear elastic functionally graded materials subjected to a thermal shock is presented. The material parameters are assumed to be continuous functions of the Cartesian coordinates. Laplace‐domain fundamental solutions of linear coupled thermoelasticity for infinite, isotropic, homogeneous and linear elastic solids are applied to derive the boundary‐domain integral equation formulation. The numerical implementation is performed by using a collocation method for the spatial discretization. Numerical results for the dynamic stress intensity factors are presented and discussed. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling of interfacial damage and delamination of sprayed coatings with cohesive elements
Authors: Roth Stephan , Kuna Meinhard
Published: December 2011

Delamination of thermally sprayed corrosion protection coatings as a consequence of thermo‐mechanical fatigue is investigated. This study focusses on the modelling of interfacial damage initiation and evolution under cyclic loading with the help of a cohesive zone model. The presented model features a slight non‐linearity at unloading from the exponential “damage locus” as well as cyclic damage accumulation restricted to (re)loading conditions. Additionally, an endurance limit is introduced indicating the maximum sustainable traction for an infinite number of load cycles. The capability of the model is demonstrated. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
From Damage to Delamination
Authors: Thomas Marita
Published: December 2011

Delamination models are derived as the limits of models for partial isotropic volume damage via dimension reduction. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Delamination of Grain‐Interfaces in Silicon Nitride
Authors: Wippler Johannes , Böhlke Thomas
Published: December 2011

Intergranular cracking due to delamination of grain interfaces along with the development of bridging grains is the most important mechanism for the high fracture toughness of silicon nitride. In this line, an interface behavior, which is extending the Coulomb friction concept into the tensile domain has been implemented into a thermodynamical consistent frame work of Helmholtz free energy and dissipation. The model is used to describe the fracture process in a simple model geometry with a β‐Si3N4 grain embedded into a precracked matrix of oxynitride glass. The material model considers the thermoelastic anisotropy of the grain and the thermal residual stresses, which evolve during the cooling of the model from the glass transition temperature to room temperature. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analytical stress analysis of partially plastic graded curved bars subjected to pure bending
Authors: Arslan Eray , Eraslan Ahmet N.
Published: December 2011

An analytical model is developed to analyze stresses in functionally graded (FGM) curved bars under pure bending. Both elastic and partially plastic stress states are considered. The modulus of elasticity of the bar material is allowed to vary. While the model is outlined, important findings are mentioned. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mechatronic Subsystem Studied of Approximate Method Modeled by Hypergraph
Authors: Buchacz Andrzej
Published: December 2011

The transverse vibrating mechatronic subsystem is considered. Integral parts of this system are: a continuous beam with known boundary conditions and a transducer, extorted by harmonic voltage excitation, to be perfectly bonded to the beam surface. Findings this article are dynamical characteristics of the discussed mechatronic and mechanical system to model them by hypergraphs. Research limitation is that the linear mechanical subsystem and linear electric subsystem of mechatronic system has been considered, however for this kind of systems the approach is sufficient. Practical implications of this researches was that global approach is presented, that means in the domain of frequency spectrum analysis. The methods of analysis and obtained results can be base of design and investigation for this type of mechatronic systems. Originality of this paper is that the mechatronic system created from mechanical and electric subsystems with electromechanical bondage has been considered. This approach is different from those considered so far because is it relies on application approximate methods of analysis of mechatronic subsystem and modeling the one by hypergraph [1‐7]. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Consistent time integration for transient three‐dimensional contact using the NTS‐method
Authors: Franke Marlon , Hesch Christian , Betsch Peter
Published: December 2011

The present work aims to investigate stable time integrators for large deformation contact problems within the framework of the well known node‐to‐segment (NTS)‐method. For this kind of problem, standard time integrators fail to conserve the total energy of the system. To remedy this drawback, we combine a mixed method with the concept of a discrete gradient applied to the aforementioned NTS‐method. In the context of nonlinear elastodynamics stable integrators for ordinary differential equations have been extensively developed and investigated during the last two decades. For contact problems, energy consistent integrators have been developed for the NTS‐method (see e.g. Ref. [1]). (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Elastic‐plastic halfspace simulation
Authors: Hauer Franz , Willner Kai
Published: December 2011

Due to the roughness of technical surfaces only the surface peaks are in contact for moderate contact pressures. Thus, the real contact area is smaller than the apparent contact area. Contact forces can only occur in the real contact area. Consequently it is necessary to determine the deformation of surface asperities in order to analyse the tribological properties of surfaces. The real contact area is usually small in initial contact. This leads to large contact pressures which in turn lead to the plastic deformation of surface roughness peaks. Therefore an elastic‐plastic model is necessary. The halfspace model seems to be beneficial because there is only a system of equations on a surface mesh to be solved and not on a volume mesh like in the Finite‐Element‐Method. This leads to a much smaller system of equations which should allow reasonable calculation times even for large contact surfaces. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Buckling Analysis of Carbon Nanotubes – a molecular mechanics approach using the finite element framework
Authors: Hollerer Stefan
Published: December 2011

In this work, a molecular mechanics model embedded in the finite element framework is applied to analyze the buckling behaviour of carbon nanotubes. Within this model a specific finite element is set up for the underlaying interatomic potential describing the behaviour of the multi particle system. The model relies on the fully nonlinear description of the interatomic potential and the atomic kinematics. Stability points of the system are located by an accompanying eigenvalue analysis and the bifurcation point is detected using a bisection algorithm. To follow the nonlinear load‐deformation path in the area of postbuckling a branch switch is performed. With the help of this molecular mechanics model, the response of carbon nanotubes on different loading conditions with respect to buckling is studied. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Dynamic Stability Analysis of Shells Using a Finite Element Based Reduction Method
Authors: Jansen Eelco , Rahman Tanvir , Gürdal Zafer
Published: December 2011

A finite element formulation of a reduction method for dynamic stability analysis of imperfection‐sensitive shell structures is presented. The reduction method makes use of a perturbation approach, initially developed for static buckling and later extended to dynamic buckling analysis. The single mode dynamic buckling analysis and its extension to parametric excitation analysis are described. The approach is available within a general purpose finite element code. Characteristic results for the parametric excitation analysis of a composite cylindrical shell are shown. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling of material and structural inhomogeneities in timber structures
Authors: Jenkel Christian , Lang Ronny , Kaliske Michael
Published: December 2011

The numerical simulation of timber structures by means of FEM has been an object of recent research. Most of the material models developed so far are based on idealized assumptions by disregarding inhomogeneities. Here, models to capture structural inhomogeneities in terms of branches and knots and the resulting deviation in grain course in a three‐dimensional FE analysis are presented. Besides, naturally varying material properties referred to as material inhomogeneities have to be considered in the structural analysis. Due to the insufficient experimental data, the uncertainty model fuzziness is applied. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of PID Control Unit for System Stabilization in Process‐integrated Powder Coating by Radial Axial Rolling of Rings
Authors: Kebriaei Reza , Frischkorn Jan , Reese Stefanie
Published: December 2011

The process integrated powder coating by radial axial rolling of rings represents a new hybrid production technique in order to apply the functional layers on ring‐shaped work pieces. Since the layer is produced in a powder metallurgical way [1], the ring volume decreases during the compaction of the layer material. In conventional ring rolling processes an isochoric plastic deformation of the ring is exploited in order to control the process. However this is not true any more for a ring exhibiting a compressible layer [2]. Consequently different control mechanisms have to be developed for the new considered process. One major aspect is the stability of the process which is governed by a stable position of the ring as well as the roundness of the ring. Therefore the finite element (FE) model has been coupled with a PID‐controller unit and it will be shown that a stable process can be reached in this way. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Asymptotic analysis of the interaction of a finite number of holes in an elastic plane or half‐plane
Authors: Kratochvil Jan , Becker Wilfried
Published: December 2011

The problem of the interaction of a finite number of holes in an elastic plane or half‐plane is considered. The analysis is based on the complex potential method of Muskhelishvili as well as on the theory of compound asymptotic expansions by Maz'ya. An asymptotic expansion of the complex potentials in terms of relative hole radii is constructed. This expansion is uniformly valid in the whole domain. The method leads to a simple procedure which does not involve any coupled system of linear equations. The successive closed‐form approximations can be obtained in an iterative manner to an arbitrary order without any need for numerical approximation. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Symmetric Galerkin Boundary Element Method for Linear Poroelasticity
Authors: Messner Michael , Schanz Martin
Published: December 2011

In linear poroelasticity so far only collocation boundary element methods have been available. However, in some applications, e.g., when coupling with finite elements is desired, a symmetric formulation is preferable. Choosing a Galerkin approach which involves the second boundary integral equation, such a formulation is possible. Here, a previously presented integration by part technique for the regularization of the first boundary integral equation is extended to the second boundary integral equation as well. While the weakly singular representation of the double layer operator has been presented before, the emphasis lies here on the so called hyper‐singular boundary integral operator. Due to the regularization, this operator can be evaluated numerically and, hence, be used within a numerical scheme for the first time. Different numerical studies will be presented to show the behavior of the established symmetric Galerkin boundary element method, also comparing it with collocation boundary element methods. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Finite Element implementation for the EULER‐EYTELWEIN‐problem and further use in FEM‐simulation of common nautical knots
Authors: Metzger Andreas , Konyukhov Alexander , Schweizerhof Karl
Published: December 2011

The computation of ropes and cable constructions considering contact as well as friction is often required in engineering practice. That includes mutual frictional contact between two and more ropes and frictional contact between ropes and solid –mostly assumed as rigid– bodies. The latter occurs especially in the mechanical model of a rope wound around a cylinder. So the main topic of this contribution is the development and FE‐implementation of a "Segment‐ To‐Analytical‐Surface (STAS)"‐contact‐element which can be used to describe the mechanical model of a rope wound around a cylinder. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear failure mechanisms of laminated composites
Authors: Völlmecke Christina , Müller Wolfgang H.
Published: December 2011

Two distinct analytical models are described representing geometrically nonlinear instabilities in layered composites under in‐plane compression — kink‐banding and delamination buckling. The utilized technique is based on of energy minimization principles in order to examine the underlying mechanics of the systems. It is demonstrated that using this approach enables investigations to be undertaken far into the postbuckling range whilst changing system parameters. Thereby a greater phenomenological understanding of the mechanics of the systems is achieved. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A comparison of time adaptive integration methods for small and large strain viscoelasticity
Authors: Rothe Steffen , Hartmann Stefan , Hamkar Ahmad‐Wahadj , Quint Karsten
Published: December 2011

In quasistatic solid mechanics the initial boundary value problem has to be solved in the space and time domain. The spatial discretization is done using finite elements. For the temporal discretization three different classes of Runge‐Kutta methods are compared. These methods are diagonally implicit Runge‐Kutta schemes (DIRK), linear implicit Runge‐Kutta methods (Rosenbrock type methods) and half‐explicit Runge‐Kutta schemes (HERK). It will be shown that the application of half‐explicit or linear‐implicit Runge‐Kutta methods can enormously reduce the computational time in particular situations. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On Neumann ‐ Dirchlet coupling strategy of Finite Element and Boundary Element method in elastodynamics
Authors: Rurkowska Katherina , Schauer Marco , Langer Sabine
Published: December 2011

The Finite Element Method (FEM) and the Boundary Element Method (BEM) are the most used numerical tools for solid mechanics analysis. Each one of these methods has advantages and drawbacks in different cases. In order to take advantage of both methods, a nonoverlapping domain decomposition method FEM ‐ BEM in elastodynamics is presented. The domain is divided in two subdomains and each one of them is analyzed separately and only the interface information is exchanged. An iterative Neumann ‐ Dirchlet algorithm with relaxation is used, to get continuity and the equilibrium conditions at the interface. The FEM time integration is carried out using the Newmark's method and the BEM approach in time domain is based in the Convolution Quadrature Method developed by Lubich. Numerical examples are presented to show agreement with other available numerical results. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Finite Cell Method for large deformation analysis
Authors: Schillinger Dominik , Ruess Martin , Düster Alexander , Rank Ernst
Published: December 2011

The Finite Cell Method (FCM) combines the fictitious domain approach with high‐order finite elements and adaptive integration. For linear elastic problems with smooth solution, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. In this contribution, the FCM idea is combined with standard finite element technology for the solution of geometrically nonlinear problems. In particular, a modified FCM formulation is introduced, which resets the deformed configuration of the fictitious domain to the deformation‐free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis with very small values of the penalty parameter, while the accuracy of the geometrically nonlinear solution within the physical domain remains unaffected. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Computation of Creep in an Axially Moving Beam
Authors: Simon Gottfried , Holl Helmut J.
Published: December 2011

Two mechanical models for an axially moving beam supported by discrete elastic springs are derived, analysed and compared. It is considered that the beam has a constant thickness, a predefined temperature distribution and a given transversal load. The first beam model applies global Ritz approximations for the spans with springs. Gauss integration points are used in longitudinal and transverse direction. The second beam model uses a conventional FE description. The thermal and pressure loads cause stresses, which lead to strain rates due to creep of the material so that a time dependent deformation between the elastic supports results. Here the axial motion is considered to be so slow so that inertia effects can be neglected. The axial transport of the inelastic creep‐strains has been considered in the computation. The temperature field is constant and fixed in space. The deflection of the axially moving beam model is computed considering a variable number of spans separated by elastic springs. The computed results of the two mechanical models are compared for a beam with two spans. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Combined asymptotic and direct approach to the nonlinear plane problem of dynamics of a thin curved strip
Authors: Vetyukov Yury
Published: December 2011

On the example problem of large elastic oscillations of a thin curved strip we present a combined modeling approach: the non‐reduced continuous problem splits asymptotically into a system of linear equations of the rod model and a problem over the thickness; direct approach to a material line provides nonlinear equations; after the numerical solution of the reduced problem we restore the distributions of stresses, strains and displacements over the thickness. Convergence to the solution for the non‐reduced continuum as the thickness tends to zero justifies the analytical conclusion that the curvature and variation of the material properties over the thickness do not require special treatment for classical Kirchhoff's rods. Further terms of the asymptotic expansion lead to a model with shear and extension, in which curvature appears in a non‐trivial way.

The results of the study are illustrated by a numerical example and provide better understanding of the relation between the solutions of the original and dimensionally reduced problems for spatial rods and shells. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Seismic collapse capacity spectra for simple structures vulnerable to dynamic instabilities
Authors: Adam Christoph , Jäger Clemens
Published: December 2011

In this study collapse capacity spectra based on various definitions of the seismic intensity are set in contrast and evaluated. The presented collapse capacities for highly inelastic non‐deteriorating single‐degree‐of‐freedom (SDOF) systems, which are vulnerable to the destabilizing effect of gravity loads, are derived for a near‐fault set of ground motions with distinct pulse characteristics. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Instability maps of a system of Mathieu‐Equations using different perturbation methods
Authors: Hubinger Stefan , Gattringer Hubert , Bremer Hartmut , Mayrhofer Karl
Published: December 2011

It is well known, that the Mathieu‐equation possesses several instability regions. Dealing with systems of Mathieu‐ equations results in an increase of the number and size of the instability regions. The so called combination frequencies, an addition of the natural frequencies of the time invariant system, appear. Applying the Floquet theory and numerical integration yields a grid of stable and unstable areas. Even if this procedure delivers good results it is not suitable for a fast calculation, because it is very CPU‐ time consuming. Therefore several Perturbation methods are compared in this paper. The first one is the Lindstedt‐ Poincaré method, delivering some of the instability areas. The second one is the Multiple‐ Scales‐ method used with an approximation up to second order. Assuming the periodicity of the equations solution, with parameters on the boundary curve, facilitates the mathematical description of the borderline. An example is carried out; the analytical stability boundaries are validated by the Floquet theory. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Study on dimension reduction methods for a fluid conveying tube
Authors: Steindl Alois
Published: December 2011

The Application of Dimension Reduction by Approximate Inertial Manifolds to the dynamics of a fluid conveying tube doesn't perform as expected due to the presence of viscous damping terms, which lead to a cluster point of stable eigenvalues. We investigate methods to circumvent the problems introduced by this cluster point: For the spectral decomposition part of the invariant subspaces are computed using the Schur factorisation. Also a different choice of basis functions for the dominating modes avoids the difficulties. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the influence of design parameters and nonlinearities in vehicle suspensions on road deformation
Authors: Vogt Heike , Hetzler Hartmut , Seemann Wolfgang
Published: December 2011

Among others, two main objectives of modern vehicle design are road friendliness and ride comfort. Both aspects are strongly related since the dynamical tire forces depend on the vertical acceleration of the vehicle. In order to investigate the influence of design and operation parameters, different car models are considered which move with constant velocity on a rippled road. First, a linear half car model is examined and the influence of different design parameters is discussed. Second, nonlinear suspensions with Coulomb friction due to sealings as well as with bilinear shock absorbers are taken into account. The vertical dynamics of the vehicle model and the dynamic tire forces between vehicle and road are calculated using analytical methods. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An extended tube model for thermo‐viscoelasticity of rubberlike materials: Parameter identification and examples
Authors: Behnke Ronny , Dal Hüsnü , Kaliske Michael
Published: December 2011

The extended tube‐model was presented by KALISKE & HEINRICH (RCT 72, 602‐632) in 1999 as a novel approach for isothermal hyperelasticity of rubberlike materials. This contribution is dedicated to its further development to finite non‐linear thermo‐viscoelasticity. A non‐linear evolution law and a thermo‐mechanical coupled free energy formulation are the kernel of the phenomenological approach where the elastic material response is inspired by statistical‐mechanical theory. The representation of viscoelasticity is based on a multiplicative decomposition of the deformation gradient. The Helmholtz free energy of the material is formulated in terms of isothermal free energy functions multiplicatively coupled with non‐linear temperature evolution functions. The non‐linear evolution law for the viscous material branch is solved by applying a predictor‐corrector algorithm with an exponential mapping scheme. In today's literature, several sophisticated thermo‐mechanical material models are available. However, they are built upon a considerable number of material parameters governing the mechanical and thermal material response which need to be identified for practical application. Therefore, particular emphasis is given to an appropriate parameter identification technique for the thermal field. For the latter, a uniaxial extension test is carried out where the recorded data of the temperature field of the rubber specimen under cyclic loading is used for parameter identification. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Collapse criteria of foam cells under various loading
Authors: Evdokymov Nikolai , Altenbach Holm , Eremeyev Victor A.
Published: December 2011

Recently porous materials are widely used in civil and mechanical engineering. In particular, such porous materials as metal and polymer foams have applications in lightweight structures. From mechanics point of view foams can demonstrate unusual behavior such as strain localization related to foam cells buckling under certain loads.

The aim of this work is the elaboration of the model of foam material taking into account the cell collapse. We consider the cell collapse initiation during the elastic instability and its further evolution under loading. The geometrical structure of foam is generated with the use of the Voronoi algorithm. Based on stochastic distributions of cells we create various geometrical models of foams. The influence of the cell volume, wall thicknesses and material properties of the foam material on critical loads is obtained. The calculations are performed with the use of Abaqus CAD/CAE system. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A comparison between inverse form finding and shape optimization methods for anisotropic hyperelasticity in logarithmic strain space
Authors: Germain Sandrine , Steinmann Paul
Published: December 2011

In this paper an inverse mechanical formulation and a Limited‐Broyden‐Flechter‐Goldfarb‐Shanno method for shape optimization are compared. Both methods deal with the determination of the undeformed shape of an hyperelastic part knowing its deformed configuration and the applied loads. We consider anisotropic hyperelastic materials that are formulated in the logarithmic strain space. Beside the theoretical aspects, we present a numerical example. We established that no difference could be found between the node coordinates on the undeformed sheets computed with both methods. However the convergence to the solution is faster for the inverse mechanical formulation compared to the L‐BFGS algorithm. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Model for the Texture Evolution in Polycrystalline Materials
Authors: Heinz Sebastian
Published: December 2011

We study a polycrystalline material that undergoes a rigid‐plastic rate‐independent evolution. Of our particular interest is the creation of texture and the resulting qualitative change in the macroscopic material response: from isotropic to anisotropic. Texture is represented by a crystal orientation distribution function, which associates every spatial point with a probability measure on the set of rotations. We discuss an energetic formulation for the texture evolution in the context of generalized standard materials. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of coupled deformation‐induced twinning and dislocation slip using incremental energy minimization
Authors: Homayonifar Malek , Mosler Jörn
Published: December 2011

The complex interplay between dislocations and deformation‐induced twinning leads to a relatively poor formability of magnesium at room temperature. For understanding the complicated behavior of this metal, a novel model is presented. It is based on a variational principle. Within this principle based on energy minimization, dislocation slip is modeled by crystal plasticity theory, while the phase decomposition associated with twinning is considered by sequential laminates. The proposed model captures the transformation of the crystal lattice due to twinning in a continuous fashion by simultaneously taking dislocation slip within both, possibly co‐existent, phases into account. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of pseudo‐plasticity in shape‐memory‐alloys
Authors: Junker Philipp , Hackl Klaus
Published: December 2011

The name shape memory originates from the material's capability to recover its original shape after an apparent plastic deformation. The secret of this property lies in the specific microstructure. During mechanical loading, alloys of this particular kind change their crystallographic structure from randomly orientated martensite to ordered martensite. With austenite as high‐temperature inter‐state induced by heat supply, a recovery from the ordered to the unordered martensite is possible. This is accompanied by a macroscopic "healing" process.

We apply our material model for shape‐memory alloys to this special property and present numerical results. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
From atomistics to the continuum: a mesh‐free quasicontinuum formulation based on local max‐ent approximation schemes
Authors: Kochmann Dennis M. , Amelang Jeffrey S. , Español Malena I. , Ortiz Michael
Published: December 2011

A novel quasicontinuum formulation based on mesh‐free local maximum‐entropy approximation schemes is presented, whose accuracy (compared to full atomistic simulations) is tunable and, in particular, can be designed superior to conventional affine approximation schemes. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Application of a Viscoelastic Model to simulate the Interface of a Metal/Fibre‐Reinforced Polymer Joint
Authors: Konchakova Natalia , Mueller Ralf , Barth Franz‐Josef
Published: December 2011

A viscoelastic model with the Lemaitre‐type damage is applied to simulate an interfacial adhesive zone in light weight engineering structures, like aluminum/fiber‐reinforced polymer specimens. The evolution of irreversible deformation and damage progression are investigated. The joint of aluminium alloy 5754 (AA5754) and carbon fibre reinforced thermoplastic composite CF‐PA66 is manufactured by means of an epoxy (1K) adhesive. The adhesive zone is considered as an interface material. The aim of the research is to study the influence of the interface geometry on the mechanical characteristics of the structure. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A material model of nonlinear fractional viscoelasticity
Authors: Müller Sebastian , Kästner Markus , Brummund Jörg , Ulbricht Volker
Published: December 2011

Multiscale methods are frequently used in the design process of textile reinforced composites. In addition to the models for the local material structure it is necessary to formulate appropriate material models for the constituents. While experiments have shown that the reinforcing fibers can be assumed as linear elastic, the material behavior of the polymer matrix shows certain nonlinearities.

These effects are mainly due to strain rate dependent material behavior. Fractional order models have been found to be appropriate to model this behavior. Based on experimental observations of Polypropylene a one‐dimensional nonlinear fractional viscoelastic material model has been formulated. Its parameters can be determined from uniaxial, monotonic tensile tests at different strain rates, relaxation experiments and deformation controlled processes with intermediate holding times at different load levels. The presence of a process dependent function for the viscosity leads to constitutive equations which form nonlinear fractional differential equations. Since no analytical solution can be derived for these equations, a numerical handling has been developed. After all, the stress‐strain curves obtained from a numerical analysis are compared to experimental results. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analysis of nanoindentation experiments by means of atomic force microscopy
Authors: H. Müller Wolfgang , Worrack Holger , Zapara Maksim
Published: December 2011

Nanoindentation is quite a common method for local material characterization. Values for hardness and Young's modulus can be determined directly from the recorded data. Essential for the correct determination of the material parameters is the precise measurement of the actual indentation depth of the indenter. The indenter measures the current depth by means of a Wheatstone bridge which correlates the indentation depth to a change in voltage. A possible tool for the verification of the recorded indentation depths is Atomic Force Microscopy (AFM). AFM is able to scan an area of indents for almost any surface. The deflection of the tip is measured by a laser spot reflected from the surface of the cantilever. The difference in height between the surface and the indent can directly be read off from the plotted image. However, using an AFM only allows us to measure the depth of the permanent indentation depth after unloading the indenter. Nevertheless, correlation between the remaining indentation depths measured by the explained methods allows for a first assessment of the correctness of the online recorded depth‐data by the nanoindenter. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Thermo‐mechanical description of material diffusion during an ultrasonic wire bonding process
Authors: Müller Wolfgang H. , Sbeiti Mohamad , Schneider‐Ramelow Martin , Geissler Ute
Published: December 2011

The volume diffusion during an ultrasonic wire bonding process leads to a material transport between the wire and the material of the substrate and thus creates an intermetallic phase between them. In order to investigate this process, the thermal and mechanical mechanisms occurring during wire bonding should be studied. For this purpose, finite element simulations based on coupled thermo‐mechanical equations are performed to study the temperature and stress distribution in and around the interface. The final objective of the model is to develop a growth law for the intermetallic phases by considering the mechanical work applied to the wire in addition to the temperature increase at the interface. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimization of elastic material parameters of sheet metal with FEMU and DIC
Authors: Schmaltz Stefan , Willner Kai
Published: December 2011

In this paper a deep‐drawing sheet steel is characterized through tensile tests with samples taken in different angles to the rolling direction. The displacement field is recorded with an optical full‐field measurement system and the deformation field is calculated by Digital Image Correlation (DIC).

The orthotropic elastic material parameters are identified through an iterative parameter optimization via Finite Element Model Updating (FEMU). In this procedure the material parameters are modified in every iteration so that the numerically computed deformation field and forces match the measured values as well as possible.

Depending on the objective function and the input values used in the optimization routine, global or only local minima exist. To show the convergence of the applied technique, two different optimization algorithms, one gradient‐based and one gradient‐free with different initial starting points were used. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An isoclinic elasto‐plasticity model at finite strains with the notion of plastic spin
Authors: Ulz Manfred H.
Published: December 2011

In forming processes metal sheets undergo large deformations. The crystallographic texture changes and preferred directions in the macroscopic behaviour are introduced as a result. This yields an anisotropic behaviour in plastic deformations and, furthermore, these preferred directions may rotate with evolution of plasticity. A phenomenological model for the description of orthotropic elasto‐plastic solids with the notion of plastic spin is developed. The latter is the spin of the continuum relative to the material substructure. A multiplicative decomposition of the deformation gradient tensor into an elastic and a plastic part serves as the basis for the formulation and computational implementation. The resulting incompatible intermediate manifold is identified in the model as an isoclinic configuration. Moreover, the described rate‐independent constitutive model is capable of modelling isotropic elastic and orthotropic plastic material behaviour. The latter is dominated by pre‐existing preferred orientations in the material and is described by a Hill‐type yield criterion. These orientations are allowed to rotate by introduction of the plastic spin into the model. Finally, numerical simulations demonstrate the performance of the model. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Plastic slip patterning through rate dependent non‐convex gradient‐enhanced plasticity
Authors: Yalçinkaya Tuncay , Brekelmans W. A. M. , Geers M.G.D.
Published: December 2011

The paper presents a non‐convex rate dependent strain gradient plasticity framework for the description of plastic slip patterning in metal crystals. The non‐convexity is treated as an intrinsic property of the free energy of the material. Departing from explicit expressions for the free energy, the non‐convex strain gradient crystal plasticity model is derived in a thermodynamically consistent manner, including the accompanying slip law. For the numerical solution of the problem, the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by solving simultaneously the linear momentum balance and the resulting slip evolution equation. The slip law differs from classical ones in the sense that it naturally includes a contribution from the non‐convex free energy term, which enables patterning of the deformation field. The formulation of the computational framework is partially dual to a Ginzburg Landau type of phase field modeling approach. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
FE‐modeling of ideal grain growth based on preprocessed EBSD data
Authors: Gladkov Slawa , Kayser Tobias , Svendsen Bob
Published: December 2011

The purpose of this work is to show the use of experimentally measured micrograph data in the context of ideal grain growth simulation which is modeled with a help of finite element method. In this regard the micrograph data is considered as initial condition for a grain growth simulation. General remarks on preparation (preprocessing) of the micrographs and staggered algorithmic formulation are presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Carbon dioxide storage in the subsurface: an approach including solid deformations and phase transition.
Authors: Häberle Kai , Ehlers Wolfgang
Published: December 2011

CO2 is supposed to be one of the major greenhouse gases. Thus, the idea arose to capture and store CO2 in the subsurface. Besides other geological formations, CO2 can be injected into deep saline aquifers, where its upward migration is blocked by an almost impermeable cap‐rock layer. It is crucial to guarantee the safety of this storage and to eliminate possibilities of leakage. Therefore, deformation processes of the rock matrix and the cap‐rock layer, which might be induced by the high pressure injection of CO2, must be investigated. The deformations may lead, on the one hand, to an increase in porosity and permeability and thereby improve the storage capacity of the reservoir. On the other hand, the increase in stress results in solid deformations of the rock matrix and may cause crack development in the cap‐rock layer. Additionally, phase transition processes between supercritical, liquid and gaseous CO2 have to be taken into account when the pressure or the temperature in the reservoir changes. The phase transition can cause an increase of CO2 volume and, hence, an increase in pressure and stress.

A continuum‐mechanical description of multiphasic flow including solid deformations is derived, which is based on the Theory of Porous Media (TPM). An elastic‐plastic material law is applied to account for the behaviour of the solid skeleton. Numerical examples are used to investigate the injection of CO2. Regions with high stresses can be identified and considered for crack initiation. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical modelling and optimization aspects of soft dielectric actuators
Authors: Klassen Markus , Xu Bai‐Xiang , Müller Ralf
Published: December 2011

Dielectric elastomer actuators (DEAs) represent a new type of actuator made of electroactive polymers which can undergo large deformations. Some applications for DEAs are: Artificial muscles, haptic feedback, pumps, robotics, deformable surfaces in aerospace, etc. For this reason the numerical modelling and optimization of DEAs represent an active field of research which supports the designing process of these actuators.

In this work the basic equations of the electro‐mechanic coupled problem are presented in a first step. Here the Neo‐Hooke and the Yeoh model have been chosen to model the behaviour of a nearly incompressible elastomer. To study optimization aspects, material inclusions in a sandwich type DEA structure have been taken into consideration. Ceramics whit high electric permittivity and air are taken into account to explore the effect of inclusions on the deformation. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)