bluuebunny/crossref_metadata_2025 huggingface dataset:
Fracture Mechanical Analysis of Cracks in Ice Shelves using the Finite Element Method and Configurational Forces
Authors: Plate Carolin , Müller Ralf , Gross Dietmar , Humbert Angelika
Published: December 2011

Ice shelves are important elements of the climate system and sensitive to climate changes. The disintegration of large Antarctic ice shelves is the focus of this fracture mechanical analysis. Ice is a complex material which, depending on the context, can be seen as a viscous fluid or as an elastic solid. A fracture event usually occurs on a rather short time scale, thus the elastic response is important and linear elastic fracture mechanics can be used. The investigation of the stress intensity factor as a measure of crack tip loading is based on a 2‐dimensional analysis of a single crack with a mode‐I type load and additional body loads. This investigation is performed using configurational forces. Depth dependent density and temperature profiles are considered. The relevant parameters are obtained by literature, remote sensing data analysis and modeling of the ice dynamics. The criticality of wet surface cracks is investigated. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Crack plane identification in anisotropic linear elastic material using the reciprocity principle
Authors: Steinhorst Peter , Sändig Anna‐Margarete
Published: December 2011

Nondestructive test methods are important for examination of elastic devices regarding existence, position and size of cracks. In the case of hidden cracks (which do not touch the boundary), a simple visual control is not sufficient. The basic idea of this paper is to examine appropriate boundary measurements under certain loads. We focus on a method presented by ANDRIEUX, BEN ABDA and BUI [1] for isotropic linear elasticity, and generalize the crack plane detection to anisotropic linear elastic material. The main idea is the use of the reciprocity principle in order to connect data from the outer boundary with the unknown crack properties. Some 2D numerical examples demonstrate, that the method is working with simulated data. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Moving Kriging Interpolation‐based Meshfree Method for Dynamic Analysis of Structures
Authors: Bui Tinh Quoc , Zhang Chuanzeng
Published: December 2011

A novel meshfree model based on the standard element‐free Galerkin method incorporated moving Kriging interpolation (MK) is developed for free and forced vibration analysis of 2D structures. Instead of employing moving least square approximation (MLS), shape functions here are constructed by the MK method. Due to the satisfaction of the Kronecker delta function, the essential boundary conditions are thus imposed directly as the finite element method and no special techniques are required. Elastodynamic equations are transformed into a standard weak formulation and then discretized into a meshfree time‐dependent equation solved by the standard Newmark time integration method. Some numerical examples of stuctural problems in 2D are attempted, and it is found that the method is adequately accurate and stable for dynamic problems. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Sensitivity study of the contact situation between the brake pad and the disc
Authors: Dombek Dominika , Ostermeyer Georg‐Peter
Published: December 2011

The contact situation between the brake pad and the disc during the braking process is of particular importance concerning the squeal behavior of brake systems. After the braking process, the surface topography of brake pads can be measured using a confocal microscope. An algorithm to calculate the contact between two surfaces has been developed at the Institute of Dynamics and Vibrations. The algorithm calculates the deflection of asperities under a normal load regarding an elastic material behavior. A normal load is applied to a measured surface topography of the brake pad; the counter body (brake disc) is represented by a flat surface. The potential contact area, the locally distributed forces, deflections and normal stiffness of the pad are computed. Since there is an uncertainty in the relative position between the pad and the disc and hence the real contact situation during the braking process is not known, different contact situations must be considered during the simulations. Concerning various tilt angles of the pad that can arise during the vibrations of the brake system, a sensitivity study has been carried out. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
FE Analysis using Recurrent Neural Networks for Uncertain Stress‐Strain‐Time Dependencies
Authors: Freitag Steffen , Graf Wolfgang , Kaliske Michael
Published: December 2011

A new soft computing approach is described, which can be applied for the identification of uncertain time‐dependent material behaviour. Artificial neural networks are utilized for model‐free material formulations. Uncertain stress‐strain‐time dependencies obtained from uncertain results of experimental investigations are described by recurrent neural networks for fuzzy data. An incremental finite element formulation is presented using neural networks instead of material models. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Structural contact problems for large deformations ‐ Comparison of steady and non steady normal field
Authors: Hammer Michael E.
Published: December 2011

We will present a comparison between two formulations of the normal vector field for contact algorithms based on the mortar method. First the non steady normal field is discussed. The non steadiness is a result of the C0 continuity of the boundary discretization. This is the common result if one discretize the domain with classical finite element methods. Second we will present results for a special normal field distribution. We average the nodal normal vector of two ascending edges and interpolate this nodal normal throughout the edges. We have implemented both methods and present comparisons based on numerical experiments. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Large deformation and stability of a shear‐deformable beam with a variable length under a uniformly distributed force
Authors: Humer Alexander
Published: December 2011

A beam held by two spatially fixed supports, may slide relative to these as soon as external loads are imposed. In particular, the possibly large deformation of a shear‐deformable beam under a uniformly distributed, transverse force is investigated, which is clamped at its left side, while it may slide horizontally through another clamping device at its right side. Consequently, the material point of the beam that is currently located at the latter and the length of the portion of the reference configuration situated in between the two supports depend on the external forces and therefore are not known in advance. In order to obtain approximate solutions, a finite element scheme is utilized, in which a coordinate transformation is introduced, by which the difficulties of non‐material boundary conditions and the unknown length of the beam are circumvented elegantly. It turns out that no static equilibrium is found, if the external forces are increased beyond a critical value, since the beam would slide out infinitely in that case. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analysis of a Compliant Mechanism for Positioning in the cm‐Range
Authors: Kern Dominik , Seemann Wolfgang
Published: December 2011

The kinematics and kinetics of a compliant mechanism are analyzed quasi‐statically. The mechanism consists of a parallelkinematic (Biglide type) with the particular feature, that its revolute joints are implemented by flexure hinges. In the considered example the flexure hinges are uniform beams similar to leaf springs. The preliminary considerations with a rigid body system and by linear theory of elasticity result in an initial geometry. In order to predict the large displacement behavior more precisely the theory of Elastica is used. An optimization method is applied to solve the mechanism's state of deformation. It was found that some aspects can be approximated by a pseudo rigid body system, while others, namely the rotation, cannot be rendered. The decreased stiffness in the highly deformed operating state appears as key problem. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of the chipping behavior of coated abrasives by cooperating cellular automata
Authors: Kummer Bastian , Ostermeyer G.‐P. , Müller M. , Fricke A. , Hoffmeister H.‐W.
Published: December 2011

During the production of high‐grade wooden components often the conditioning with coated abrasives composes the end of the process train. The chipping process and the resulting wood surface are depending of the scatter pattern parameters (particle size and distribution, …) and their time depending variations. Till now, no models exist concerning the interaction of the scatter pattern with the grinding process, the work piece surface and the clogging. The developed model is based on cooperating cellular automata. One is describing the sandpaper, the other one the work piece. These two automata interacts witch each other. Update rules are designed by physical laws and measurements. The paper shows surprising results with respect of surface structures which are the result of self‐organization effects in the boundary layer of wood and sandpaper. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Fundamental solutions for a partially saturated poroelastic continuum
Authors: Li Peng , Schanz Martin
Published: December 2011

The Boundary Element Method is quite suitable for solving dynamic semi‐infinite or infinite linear problems. In order to establish the boundary integral equations, one crucial condition is the knowledge of corresponding fundamental solutions. For a partially saturated poroelastic continuum, the governing equations in Laplace domain are formulated based on the theory of mixtures, and the related fundamental solutions are derived by using Hörmanders method. The singular behavior of the fundamental solutions are investigated by a series expansion with respect to the variable r. Finally, some exemplary fundamental solutions are calculated to visualize the principal behavior as well, and comparisons with the related results of saturated poroelasticity are given. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Applications of Rosenbrock‐type methods to the p‐version of finite elements
Authors: Netz Torben , Hartmann Stefan , Hamkar Ahmad‐Wahadj
Published: December 2011

In quasistatic solid mechanics the spatial as well as the temporal domain need to be discetized. For the spatial discretization usually elements with linear shape functions are used even though it has been shown that generally the p‐version of the finite elemente method yields more effective discretizations, see e.g. [1], [2]. For the temporal discretization diagonal‐implicit, see e.g. [4], and especially linear‐implicit Runge‐Kutta schemes, see e.g. [5], [6], have for smooth problems proven to be superior to the frequently applied Backward‐Euler scheme (BE). Thus an approach combining the p‐version of the finite element method with linear‐implicit Runge‐Kutta schemes, so‐called Rosenbrock‐type methods, is presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mechatronic system with shunted piezoelectric damper modelled with structural damping
Authors: Buchacz Andrzej , Płaczek Marek
Published: December 2011

Paper presents analysis of an one‐dimension flexural vibrating mechatronic system. The considered system is a cantilever beam with a piezoelectric transducer bonded to the beam's surface. An external electric circuit is adjoined to the transducer's clamps in order to damp vibrations. System was analyzed on the basis of an approximate Galerkin method. Verification and assumptions of the approximate method were described in the previous papers where analysis of the mechatronic system with piezoelectric shunt damper was presented. Structural damping of all system's components was being taken into consideration. Rheological properties were introduced using Kelvin‐Voigt model of materials. Influences of component's structural damping coefficients values on the system's dynamic flexibility were defined. Obtained results were presented on 3D graphs as dynamic flexibility dependence on the structural damping coefficient and frequency of an external force that was applied to the system. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Inelastic behavior of the single domain of metal‐ceramic composites with lamellar microstructure
Authors: Sinchuk Yuriy , Piat Romana , Roy Siddhartha , Gibmeier Jens , Wanner Alexander
Published: December 2011

Metal‐ceramic composites are widely applied in the different brunches of industry. The composites are produced by squeeze‐casting of the ceramic preform by molten aluminum alloy. The lamellar microstructure is obtained during freezing of ceramic suspension. The internal structure of the domains can be controlled via freeze‐casting parameters. The material has high anisotropy level and its effective properties depend on lamella orientation. The aim of this study is numerical simulation of the inelastic behavior of the material and its verification by experiment. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Weighted Least‐Squares Mixed Finite Element Formulation for Quasi‐Incompressible Elastodynamics
Authors: Steeger Karl , Schwarz Alexander , Schröder Jörg
Published: December 2011

The purpose of this work is the application of the least‐squares finite element method to an elastodynamic, quasi‐incompressible problem under small strain assumptions. Therefore a mixed finite element based on a weighted least‐squares formulation is developed. The L2‐norm minimization of the time‐discretized residuals of the given first‐order system of partial differential equations leads to a functional depending on displacements and stresses. In the numerical example the proposed mixed element is compared to an alternative approach, which is based on a least‐squares mixed finite element with improved momentum balance, see [1]. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Verification of an optical metrology system (ARAMIS) by comparing experimental data with FE calculations and continuum approaches
Authors: Stier Bertram , Reese Stefanie
Published: December 2011

Optical 3D field measuring systems, based on DIC (Digital Image Correlation) deliver kinematic quantities. They are appropriate devices helping to understand the material behavior especially at high strains. One problem of these systems is the missing information about material points located behind the observed surface of the specimen, which is needed to assign the full deformation gradient. Different ways of dealing with raw point coordinate data that is confidently given by the metrology system lead to different kinematic results. To ensure the correctness of strain‐like results determined by the system, they are compared to analytical and finite element calculations. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Parameter identification for nonlinear dynamical systems using Multi Harmonic Balance techniques
Authors: Süß Dominik , Willner Kai
Published: December 2011

An usual approach to investigate nonlinear systems in the frequency domain is the application of the Harmonic Balance Method (HBM), assuming that a harmonic excitation of the system leads to a harmonic response. However, for systems where the steady state response is not just harmonic but periodic or for systems which are excited periodically, this assumption does not longer lead to satisfying results. Therefore, the Multi Harmonic Balance Method (MHBM) is utilized. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An error indicator for parameter identification with stabilized mixed tetrahedrals
Authors: Widany Kai‐Uwe , Mahnken Rolf
Published: December 2011

The identification of parameters in constitutive laws considering inhomogeneous states of stress and strain is realized by iteratively minimizing a least squares functional. In each iterative step of this optimization problem a finite element analysis is carried out which results in a significant higher numerical cost than a single finite element analysis. Consequently, an efficient discretization is required to keep the numerical cost low. To address this problem an adaptive mesh refinement is considered which is based on a posteriori error indicators [1] leading to refinements appropriate to the parameter identification problem. The goal is to apply the error indicators to the finite element method for tetrahedral elements of low order which are preferable for adaptive mesh refinements and in addition reduce computational effort. Additional stabilization terms in the element formulation [4, 6] reduce volume locking effects making the elements suitable for (nearly) incompressible material behavior. Numerical examples illustrate the progress on this work. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On stability and self‐excited vibrations in fluid‐structure‐interaction
Authors: Bach Karolina , Hetzler Hartmut , Seemann Wolfgang
Published: December 2011

In flexible channels conveying fluid the steady state may loose stability by divergence or flutter. The aim of this contribution is to investigate the basic excitation mechanisms of flow‐induced vibrations and to evaluate the influence of various parameters on the stability behaviour of the coupled problem. Therefore, a simple, yet general model is proposed. The fluid is assumed to be inviscid and irrotational and both incompressible and compressible flow is considered. It is guided by a planar, rectangular channel with a rigid wall and a thin, flexible wall. The latter is modelled as a one‐parametric continuum on an elastic foundation, which exhibits bending and extensional stiffness. By examining the energy balance over one oscillation circle it is possible to reveal the mechanisms of energy transfer between the coupled components of the system. Based on this analysis a physical explanation of the arising instabilities is possible. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of friction phenomena between randomly rough elastic surfaces
Authors: Gaus Nicole , Proppe Carsten
Published: December 2011

Friction induced vibrations are a widely studied field in which the friction coefficient is one of the most important parameters. Measurements show that the friction coefficient underlies stochastic fluctuations. To gain more knowledge about the friction coefficient a finite element study is carried out in order to simulate the friction forces. The Bowden‐Tabor model is implemented which calculates the friction force as the force which is needed to shear apart contact areas hold together by welding or adhesion. The dependency of the friction value on sliding velocity and normal pressure can be determined with this model. Different realization are studied and the stochastic properties of the friction value such as mean value, standard deviation, amplitude spectrum and correlation coefficient can be calculated depending on the roughness of the surface. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear vibrations of elastic beams with external general visco‐elastic devices
Authors: Heuer Rudolf , Pirrotta Antonina
Published: December 2011

Vibration damping for slender beams is achieved by applying devices at external points. The latter consist of general single visco‐elastic springpot elements. An approximate nonlinear boundary value problem is found in frequency domain that holds for moderately large vibrations or for linear beams with external nonlinear devices, both in the vicinity of primary resonances. The interaction force of a so‐called springpot element is expressed as a sum of two separate forces: the first develops due to the external loading function at the device location, and the second contribution arises due to an imposed time‐harmonic support excitation with no other external forces acting on the structure. Finally the nonlinear frequency response function follows from a (nonlinear) algebraic equation where the influence of the springpot element appears as isolated parameter. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling aspects and numerical analysis of offshore systems
Authors: Jesussek Mathias , Ellermann Katrin
Published: December 2011

There is a strong effort to improve the efficiency of renewable energy systems in order to reduce the CO2 emissions. This paper addresses an approach to increase the efficiency of an ocean wave energy plant with a model based predictive controller. For this controller it is necessary to have a prediction of the ocean waves and a model of the whole system. The future development of the ocean waves is predicted by an AR‐model. A system identification yields the model of the energy plant. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Investigations on the numerical solution of the Fokker‐Planck equation with discontinuous Galerkin Methods
Authors: Loerke Friederike , Nackenhorst Udo
Published: December 2011

Nonlinear dynamic systems under stochastic excitation possess Markov characteristics. Thus, their stochastic equation of motion can be transformed into the Fokker‐Planck equation which describes the evolution of the probability density. A discontinuous Galerkin (DG) method is applied to solve the Fokker‐Planck equation. This method provides numerical stability as well as accuracy and is able to treat discontinuities of the solution. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Rayleigh quotient iteration for quadratic eigenvalue problems
Authors: Miller Urs , Gaul Lothar
Published: December 2011

For the direct solution of quadratic eigenvalue problems of the form (λ2M + P + Q)x = 0, a generalization of the Rayleigh quotient iteration is presented. Numerical simulations show good convergence for problems where the eigenvalues have nonzero imaginary part. The method is used to calculate eigenvalue paths of parameter dependent problems in structural dynamics. Bifurcations with double eigenvalues, which can occur in the path, are passed by using a perturbation of the velocity dependent matrix P. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear dynamic effects in automotive clutches
Authors: Tikhomolov Arsenty , Fidlin Alexander
Published: December 2011

Dynamic effects appearing in the dry friction clutches are very complex. The reason for this is the usual design of the clutches including complex two dimensional friction, unilateral contacts and nonlinear springs. The final quality of the clutch system for a customer depends among other criteria on the awareness of dynamic effects, which can affect functioning and comfort negatively.

One of the usual nonlinear dynamic effects in the friction clutch is presented in this work. That is the problem of dynamic disengagement which can cause significant safety problems. First of all the global nonlinear dynamic behavior is considered roughly by means of an analytical approach. Secondly a MBS‐model, which includes not only the nominal design of the clutch system but also dispersion of several parameters, is used in order to identify the influence of the asymmetry on the dynamic behavior. Analytical and numerical results are compared with measurements. Finally a possible solution of the considered problem is presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A finite element model for biofilm volume growth
Authors: Bolea Albero Antonio , Böl Markus
Published: December 2011

In this work, we present a continuum‐based approach for biofilm volume growth. The deformation gradient will be multiplicatively decomposed into two parts: a growth part due to bacteria formation and an elastic part due to the interaction with the environment. In order to define the growth behaviour of biofilms, we use the Monod approach that depends non‐linearly on the substrate concentration. The substrate concentration in the biofilm is computed by means of a diffusion process, which includes substrate consumption, together with the mechanical behaviour as part of a coupled problem. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A finite element formulation of a viscoelastic model for dielectric elastomers
Authors: Bueschel Alexander , Klinkel Sven , Wagner Werner
Published: December 2011

Smart materials by definition, are solids, fluids or gases which react independently on changing external conditions and modify one or more properties without external stimuli. Sensu lato an external energy can produce the reaction, such as stress, temperature, moisture, pH, magnetic or electric fields. The distinguishing characteristic for electroactive polymers (EAP) is, that they react with a deformation by the application of an electrical field. This contribution presents a nonlinear electro‐viscoelastic model for dielectric elastomers and its finite element implementation. This type of smart materials belong to the group of EAP's and consists out of soft elastomer between compliant and conducting electrodes. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Constitutive modelling of adhesively bonded joints
Authors: Burbulla F. , Matzenmiller A.
Published: December 2011

The non‐associated I1‐J2‐plasticity model accounts sufficiently well for the different mechanical behaviour of crashoptimized high‐strength adhesives under combined shear and tensile loading. This model is extended to material softening due to damage, rate‐dependency and a constitutive description for the mechanical behaviour of adhesively bonded joints under compression. The material parameters are identified by means of the FE‐analysis for the experimental setup of a sample of bluntly glued double tubes. A comparison of the simulated results with the experimental data proves the validity of the model. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of Deep Drawing of Carbon Fibre Prepregs
Authors: Hankeln Frederik , Mahnken Rolf
Published: December 2011

The simulation of prepregs must regard highly anisotropic, viscoelastic and thermal‐chemical properties. To this end a constitutive model is split into an anisotropic elastic part, which represents the fibre fraction and an isotropic, viscoelastic part, representing the matrix. The second part also contains curing, causing a dependency on time and temperature. During real deep‐drawing processes large deformations up to 50 % occur, which is considered in a formulation at large strains. This model contains an anisotropic elastic part based on a Neo‐Hooke law enhanced by an anisotropic part. A viscoelastic part is added using Hencky‐strains and the work‐conjugate Hill‐stress to transfer a model for small strains into large strains. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Extension of the Arruda‐Boyce model to the modelling of the curing process of polymers
Authors: Hossain Mokarram , Steinmann Paul
Published: December 2011

A phenomenologically motivated finite strain general framework to simulate the curing of polymer have been developed and discussed in our recently published papers [2,4]. The Arruda‐Boyce model is a classical hyperelastic model for polymeric materials. This contribution presents an extension of the Arruda‐Boyce model towards modelling the curing process of polymers following our previous framework. In this paper, we will show how to model the elastic behaviour and shrinkage effects of the polymer curing process in the isothermal case using the Arruda‐Boyce model. Several numerical examples have been demonstrated to verify our newly proposed modified approach in case of curing process. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A homogenization method for heterogeneous materials using a multi‐scale technique
Authors: Müller Wolfgang H. , Brandmair Andreas
Published: December 2011

For modern microelectronics solders lifetime and stability predictions are important. To perform such an analysis material properties are required. As electronic devices and the corresponding amount of matter used become smaller, the influence of a changing microstructure on mechanical properties must be considered. First some analytical methods were conducted for upper and lower bounds ignoring the exact geometric distribution of the solder phases. Second, analytical equations derived for geometries such as laminate structures were applied to examine the influence of the geometry on homogenized properties. Third, a multi‐scale approach for periodic media was presented allowing for a more general analysis of structures. We assume that the solder material is composed of periodic cells, which represent the properties of the whole structure. Composite materials with periodic structures can be investigated by using at least two scales. A global scale is related to the whole piece of material whereas a local scale is related to the periodic cell only. The constitutive equations are stated and a homogenization technique for the elastic properties of arbitrary structures is derived. The resulting equations are solved numerically and results are presented. Again, for layered materials closed‐form formulas are derived and compared to the numerical results. The method is also used to obtain effective mechanical properties for materials with linear hardening. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Dislocation Transport in Single Crystals and Dislocation‐based Micromechanical Hardening
Authors: Wulfinghoff Stephan , Glavas Vedran , Böhlke Thomas
Published: December 2011

The higher‐dimensional kinematical dislocation continuum theory of Hochrainer (2006) and a homogenized version thereof by Hochrainer, Zaiser and Gumbsch (2010) are reviewed. A three‐dimensional Finite Element solution of the homogenized theory is presented, interpreted physically and compared to the results of the Geometrically Necessary Dislocations theory. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiphase Field Modeling Chemical Vapor Infiltration of SiC/SiC Composite
Authors: Zhu Yaochan , Schnack Eckart , Li Aijun
Published: December 2011

A novel multiphase field model is formulated to describe the complex microstructure evolution during Chemical Vapor Infiltration(CVI), which is one of the important method to produce the SiC matrix composites reinforced by SiC fibers in ceramic engineer. The model is composed of a set of nonlinear partial differential equations by coupling Ginzburg‐Landau type phase field equations with mass balance equation. Mathematically, the codeposition of SiC, Si and C during CVI process is a typical free boundary problem. When this problem is handled by multiphase field method, it's greatly facilitated because of the implicitly boundary‐tracking technique by phase field order parameters. This typical multiphysic field problem is solved by finite element software COMSOL. The numerical results show good agreement with experimental research. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of Capillary Effects and Phase Transition under Freezing and Thawing Load in Liquid and Gas Saturated Porous Media
Authors: Bluhm Joachim , Bloßfeld Wolfgang Moritz , Ricken Tim
Published: December 2011

In this article, a quadruple macroscopic model for the simulation of freeze‐thaw cycles in liquid‐ and gas filled porous media is presented. Attention is paid to the description of capillary effects and phase transition. In effect, this model describes the following aspects: expansion of ice during freezing, liquid and gas pressure on the surrounding surfaces, capillary effects, temperature distribution, and the influence of filter velocities. The illustrated results of the numerical example show that the simplified model is capable of predicting physical and experimental observations. Besides the influence of heat of fusion, especially, capillary suction as well as frost suction in liquid‐ and gas filled porous media under cycling thermal loading will be presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A FEM‐BEM approach for Fluid‐Structure Interaction
Authors: Brändli Silvan , Abdel‐Maksoud Moustafa , Düster Alexander
Published: December 2011

In an earlier attempt to solve problems of Fluid‐Structure Interaction (FSI), a high‐order finite element code, which can be applied to solve problems of Computational Structural Dynamics (CSD) has been coupled to a Lattice Boltzmann (LB) fluid solver. In order to extend this approach to maritime applications and to increase the computational efficiency, the CSD solver is coupled to a fluid solver based on the Boundary Element Method (BEM). In this way, the computational effort for the discretisation of the fluid is significantly reduced. In this paper the proposed coupling scheme is discussed and compared to a FSI scheme where the BEM is replaced by a method based on the Reynolds‐averaged Navier‐Stokes equations (RANSE). Special emphasis is placed on the question of how to exchange the data between the different discretisation schemes and the development of a stable and efficient coupling scheme for FSI simulations. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A cellular automaton model for boundary friction of PEEK and PEEK6
Authors: Bubser Florian , Ostermeyer G.‐P.
Published: December 2011

Nowadays a common material for journal bearings is PEEK (Polyetheretherketon) which is increasingly used under boundary friction. A Cellular Automaton model is developed to describe the boundary layer dynamics of PEEK and its composite PEEK6 sliding against a steel surface. Whereas PEEK is a homogeneous synthetic material, PEEK6 contains also carbon fibres for stability and fillers working as solid lubricants. The automaton shows a representative area of the real surface. The processes in the interface are described by a set of rules based on physical assumptions and measurements. Based on these rules the simulations show the dependency of friction and wear on the load spectrum. The discrete simulation allows to observe the topographic development of the PEEK and PEEK6 surface as well as the build‐up of a transfer film on the steel surface. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical Simulation of Free Surface‐Structure‐Interaction with Multi‐Regional Mesh Deformation
Authors: Fuchs Vilmar , Wünsch Olaf
Published: December 2011

The Fluid‐Structure‐Interactions (FSI) for technological constructions on sea are becoming nowadays very important in view of growing consumption of renewable energy sources. Exceptionally the offshore wind farms are exposed to extreme weather conditions due to breaking and non‐breaking wave loads. This work presents numerical Finite‐Volume‐Method (FVM) analysis of fluid and structure interactions with water waves impact on elastic solid structures. We develop a Free Surface‐Structure‐Interaction (FSSI) solver in OpenFAOM [1] with multi‐regional mesh deformation. A two dimensional numerical water impact model on a damping element prototype of an offshore wind turbin tower is investigated. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Two‐dimensional analysis of a crack in quasicrystal materials
Authors: Gao Yang , Ricoeur Andreas , Zhang Liangliang
Published: December 2011

The two‐dimensional problem of a crack in three‐dimensional quasicrystals subject to far field loadings is studied. The analysis is based on the generalized Lekhnitskii's formalism. The analytical expressions for both the entire fields and the asymptotic fields near the crack tip are determined. The fracture quantities of quasicrystals, i.e., field intensity factors, energy release rates and so on, is a prerequisite. Numerical results for a Griffith crack under phason loading Mode I and II conditions are poltted. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Micro‐Electro‐Elastic Modeling of Electric Field‐ and Stress‐Driven Domain Wall Motion
Authors: Zäh Dominic , Rosato Daniele , Miehe Christian
Published: December 2011

Recently, increasing interest in functional materials such as piezoceramics has been shown. Such materials are characterized by properties, which can be significantly changed by external stimuli, such as stress, electric or magnetic fields. We outline a micro‐electro‐elastic model for the evolution of electrically and mechanically poled domains incorporating the surrounding free space. To this end, recently developed incremental variational principles (Miehe & Rosato [1]) for local dissipative response need to be extended to gradient‐type phase‐field models, including an embedding into the free space. The variational setting serves as a natural starting point for a compact and symmetric finite element implementation, considering the mechanical displacement, the electric polarization treated as an order parameter, and the electric potential induced by the polarization as the primary variables. The latter is defined on both the solid domain as well as the surrounding free space. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical modelling of coupling mechanisms during freezing in porous materials
Authors: Zhou Mengmeng , Meschke Günther
Published: December 2011

Freezing of porous materials is of interest for a wide range of engineering disciplines such as civil‐, geotechnical and environmental engineering as well as food industry. The freezing process is characterized by various couplings between the phase transition and the liquid transport within the pore space, accompanied by considerable deformations. This paper presents a macroscopic three‐phase finite element model of liquid‐infiltrated porous media subjected to freezing. For the description of the associated coupled thermo‐hydro‐mechanical behavior, the governing balance equations of the problem are formulated based upon the constitutive relations derived within the framework of thermo‐poro‐elasticity. The applicability of the model is shown by a simulation example of artificial ground freezing with coupled thermal‐hydro‐mechanical processes. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Asymptotics for a thin elastic fiber in contact with a rigid foundation
Authors: Bare Zoufine , Orlik Julia
Published: December 2011

In this work a 3‐D contact elasticity problem for a thin fiber and a rigid foundation is studied. We describe the contact condition by a linear Robin‐boundary‐condition (by meaning of the penalized and linearized non‐penetration and friction conditions). The Robin parameters are scaled differently in the longitudinal and cross‐sectional directions. The dimension of the problem is reduced by a standard ([3], [4]) asymptotic approach with an additional expansion suggested to fulfil the contact conditions. The 3‐D contact conditions result into 1‐D Robin‐boundary‐conditions for corresponding ODEs. The Robin‐coefficients of the 1‐D problem depend on the ones from the 3‐D statement and on the cross‐section of the fiber. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Microscale modelling and homogenization of fiber structured materials
Authors: Fillep Sebastian , Steinmann Paul
Published: December 2011

Various phenomena occurring on the macrosscale result from physical and mechanical behaviour on the microscale [1]. For the mechanical modeling and simulation of the heterogeneous composition of fiber structured material, in addition to the material properties the contact between the fibers has to be taken into account. The material behaviour is strongly influenced by the material properties of the fiber, but also by the geometrical structure. Periodically arranged fibers like woven, knitted or plaited fabrics and randomly oriented ones like fleece can be distinguished in their arrangement. In consideration of different lengthscales the problem involves, it is necessary to introduce a multiscale approach based on the concept of a representative volume element (RVE). The macro‐micro scale transition requires a method to impose the deformation gradient on the RVE by suited boundary conditions. The reversing scale transition, based on the HILL‐MANDEL condition, requires the equality of the macroscopic average of the variation of work on the RVE and the local variation of the work on the macroscale [2]. For the micro‐macro transition the averaged stresses have to be extracted by a homogenization scheme. From these results an effective material law can be derived. Beside the theoretical aspects, we present the stress‐strain relation for RVE‐models and different boundary conditions. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear homogenization using the nonuniform transformation field analysis
Authors: Fritzen Felix , Böhlke Thomas
Published: December 2011

The homogenization of physically nonlinear composite materials with anisotropic morphology is investigated using the nonuniform transformation field analysis (NTFA) first introduced by [1, 2]. In this contribution a three‐dimensional finite element implementation (see [3]) of the NTFA is used for the homogenization of composite with morphological anisotropy (see also [4]). The main focus is on the application to structural problems with spatially varying orientation of near‐spherical and needle‐shaped particle reinforcements. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive Multi‐scale Modeling Error Estimation for Composites
Authors: Hajibeik Nasim , Temizer İlker , Löhnert Stefan , Wriggers Peter
Published: December 2011

Abstract Analysing composite materials through efficient higher‐order homogenization techniques requires accurate simulations of highly heterogeneous domains. However the validity of the homogenization response in regions with highly localized variations is still questionable. A scale adaptation strategy is developed for a more accurate analysis of generally inelastic macrostructures, where a transition from a homogenized description to an explicit micro‐structural resolution is pursued. The designated zones of interest are indicated through two different methods of error estimation. First for mesh refinement approaches, the discretization error is estimated using an indicator developed by Zienkiewicz‐Zhu and studying L2 norm. Furthermore a second adaptation zone is identified based on a post‐processing step on the homogenized solution and corresponds to regions with high strain‐gradients, the gradient of the deformation gradient. In the designated sub‐domains a micro‐structure representation will replace the homogenized area. The introduced scale‐adaptivity method returns an inexpensive and more accurate analysis of composite materials. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Configurational forces in a multiscale approach to piezoelectric materials
Authors: Khalaquzzaman Md. , Müller Ralf , Ricker Sarah , Xu Baixiang
Published: December 2011

Due to the growing interest in determining the macroscopic material response of inhomogeneous materials, computational methods are becoming increasingly concerned with the application of homogenization techniques. In this work, a two‐scale classical homogenization of an electro‐mechanically coupled material using a FE2‐approach is discussed. We explicitly formulated the homogenized coefficients of the elastic, piezoelectric and dielectric tensors for small strain as well as the homogenized remanent strain and remanent polarization. In the homogenization different representative volume elements (RVEs), which capture the micro‐structure of the inhomogeneous material, are used to represent the macroscopic material response. Two different schemes are considered. In the first case, domain wall movement is not allowed, but in the second case the movement of the domain walls is taken into account using thermodynamic considerations. Later this technique is used to determine the macroscopic and microscopic configurational forces on defects [2]. These defect situations include the driving force on a crack tip. The effect of the applied electric field on configurational forces at the crack tip is investigated. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling and numerical simulation of multiscale behavior in polycrystals via extended crystal plasticity
Authors: Klusemann Benjamin , Bargmann Swantje , Svendsen Bob
Published: December 2011

The purpose of this work is to exploit the algorithmic formulation of models for multiscale inelastic materials whose behavior is influenced by the evolution of inelastic microstructure and the corresponding material or internal lengthscales. The models for extended crystal plasticity are based on the formulation of rate potentials whose form is determined by (i) energetic processes via the free energy, (ii) kinetic processes via the dissipation potential, and (iii) the form of the evolution relations for the internal‐variable‐like quantities upon which the free energy and dissipation potential depend. Examples for these latter quantities are the inelastic local deformation or dislocation densities as GNDs. Different algorithmic implementations are discussed, namely the algorithmic variational approach and the dual mixed approach. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Estimate of the Domain Orientation Distribution Function and the Thermoelastic Properties of Pyrolytic Carbon Based on an Image Processing Technique
Authors: Lin S. , Böhlke T. , Langhoff T.‐A.
Published: December 2011

The microstructure of Pyrolytic Carbon (PyC) can be described as an aggregate of coherent domains with different orientations. The domains exhibit an approximately a hexagonal material symmetry. In order to apply statistical homogenization schemes which predict the thermomechanical properties in terms of the microstructural characteristics, a quantitative description of PyC microstructures based on the domain orientation distribution function (DODF) is introduced in this work. The von‐Mises Fisher distribution is applied for modeling the orientation of the unit normal vectors of the graphene planes. The respective probabilty density function depends on the so‐called concentration parameter κ. The parameter κ is estimated by the set of domain orientations, which can be obtained by applying the image processing technique. This procedure facilitates the estimate of the 2nd order bounds (Hashin‐Shtrikman upper and lower bounds) based on the real microstructure. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Validation of Material Models in Grain Scale Simulation based on EBSD Experimental Data
Authors: Van Tung Phan , Jöchen Katja , Böhlke Thomas
Published: December 2011

A crystal plasticity model and a homogenization method are used to analyze the local and global mechanical behavior of a ferritic stainless steel. In the first step the material constants are determined based on tensile tests and used to simulate the local deformation behavior on the grain scale in the second step. For that 2D EBSD data are discretized by finite elements. The computed local grain reorientations of three different BCC slip systems are compared to experimental data at the state of 20% elongation. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical homogenization of composite structures with rhombic fiber arrangements
Authors: Würkner Mathias , Berger Harald , Gabbert Ulrich
Published: December 2011

A numerical procedure is developed to determine effective material properties of unidirectional fiber reinforced composites with rhombic fiber arrangements. With the assumption of a periodic micro structure a representative volume element (RVE) is considered, where the phases have isotropic or transversely isotropic material characterizations. The interface between the phases is treated as perfect. The procedure handles the primary non‐rectangular periodicity with homogenization techniques based on finite element models. Due to appropriate boundary conditions applied to the RVE elastic effective coefficients are derived. Six different boundary condition states are required to get all coefficients of the stiffness tensor. Results are listed and compared with other publications and good agreements are shown. Furthermore new results are presented, which exhibit the orthotropic behavior of such composites caused by the rhombic fiber arrangement. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)