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  • 2010-2014  (490)
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  • 1
    Publication Date: 2013-02-09
    Description: Common structural optimisation problems consist of problem-specific objective functions which have to be minimised mathematically with respect to design and state variables taking into account particular constraints. In contrast to this, we adopt a conceptually different approach for the design of a structure which is not based on a topology-optimisation technique. Instead, we apply a one-dimensional energy-driven constitutive evolution equation for the referential density–originally proposed for the simulation of remodelling effects in bones–and embed this into the micro-sphere-concept to end up with a three-dimensional anisotropic growth formulation. The objective of this contribution is to investigate this approach with emphasis on its application to structural design problems by means of two three-dimensional benchmark-type boundary value problems. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 2
    Publication Date: 2013-02-09
    Description: The present work aims at the modelling and simulation of Internal Traverse Grinding of hardened 100Cr6/AISI 52100 using electro plated cBN grinding wheels. We focus on the thermomechanical behaviour resulting from the interaction of tool and workpiece in the process zone on a mesoscale. Based on topology analyses of the grinding wheel surface, two-dimensional single- and multigrain representative numerical experiments are performed to investigate the resulting load-displacement-behaviour as well as the specific heat generation due to friction and plastic dissipation. A thermoelastic-viscoplastic constitutive model is used to capture thermal softening of the material taken into account. Based on previous work, an adaptive remeshing scheme which uses a combination of error estimation and indicator methods, is applied to overcome mesh dependence. In consequence, the formulation allows to resolve the complex deformation patterns and to predict a realistic thermomechanical state of the resulting workpiece surface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 3
    Publication Date: 2013-11-30
    Description: Landfill gas is composed of methane (CH 4 ) and (CO 2 ) at a ratio of about (60% – 40%), whereby the impact of methane on the greenhouse effect is about 25 times higher than that of carbon dioxide. Bacterial methane oxidation, taking place in the landfill cover layer, helps to reduce the climate active emissions from landfill sites. This contribution presents a theoretical and numerical approach to model the coupled processes of bacterial methane oxidation. An isothermal biphasic model based on the Theory of Porous Media (TPM) and Mixture Theory is introduced as well as the coupled finite element (FE) calculation concept. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 4
    Publication Date: 2013-11-30
    Description: The injection of supercritical CO 2 into deep saline aquifers is regarded as one possible alternative to lessen the impact of emitted CO 2 on the greenhouse effect. During injection, a great variety of thermodynamical and mechanical changes of both the fluid phases and the porous solid matrix can be expected. The prediction of these processes is crucial to prevent from critical incidents during CO 2 injection, such as leakage of CO 2 or contamination of drinking water. For simulation purpose, a macroscopic, fully coupled description of multi-phasic flow inside a deformable porous medium based on the Theory of Porous Media (TPM) is generated. Appropriate constitutive relations are applied to account for changes in the fluid properties of both the saline water and CO 2 during injection and leakage. Furthermore, an elasto-plastic description of solid deformations of the porous matrix is included. The model is tested based on a benchmark problem. Therein, the leakage of CO 2 through an abandoned well after injection is investigated. The fully coupled approach between fluid flow and solid deformation allows additional results to be gained from the simulation. Quantification of the leakage rate through the abandoned well and localisation of phase-change events are addressed to calibrate the presented model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 5
    Publication Date: 2013-11-30
    Description: The transitional and turbulent flow in the near wall sublayer is now mostly modeled based on the existing knowledge of simple 2D flows. To determine the effect of three dimensionality on the turbulent flow structures and turbulent heat transfer in the near wall areas the authors investigate numerically (SVV) turbulent flow in rotor/stator and rotor/rotor flows (with and without axial throughflow). These simple model flows contain most of the phenomena that are needed to understand more complex, 3D transitional and turbulent flows. Attention is focused on the turbulent characteristics which should have more universal character. To stabilize calculations for high Reynolds numbers (up to Re=800 000) the SVV operator is introduced into the Navier-Stokes and energy equations solver for cylindrical coordinate system without using complex numbers. Code optimization and parallelization have speeded up computations 20 times. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 6
    Publication Date: 2013-11-30
    Description: In this essay a fully coupled, monolithic thermo-mechanical coupled simulation using high-order finite elements based on hierarchical shape-functions in combination with a high-order time-integration scheme using diagonally-implicit Runge-Kutta schemes is presented. The constitutive model is based on a finite strain thermo-viscoelasticity relation of overstress-type. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 7
    Publication Date: 2013-11-30
    Description: In this work we present a novel approach to the modeling of magnetorheological elastomers (MREs) for finite deformations. Keeping in mind the composite nature at the microscale, we employ the microsphere model as an effective tool to capture the constitutive response of the material. The microsphere model has been successfully applied to the modelling of rubber-like materials. Here, we extend this approach by taking into account the effect of the magnetic dipole-dipole interactions on the orientation of the polymer chains. Thus, the presented microsphere model is directly motivated by considering the underlying phenomena at the microscale level. Finally the material model is embedded in a finite element framework and the results of a boundary value problems is presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 8
    Publication Date: 2013-11-30
    Description: Finite element simulation of hot working of steel has gained significant importance in steel industries. The aim of describing such processes using the finite element method is to predict phenomena like shrinkage during solidification. Due to this thermo-mechanical behaviour residual stresses appear, which cause cracks and the final steel slab loses its required properties as a result. We propose a two-phase incompressible model based on the Theory of Porous Media (TPM) for a numerical description of steelmaking processes. A thermo-mechanical coupling is required to model a high temperature-dependency. In order to consider thermal expansion of solid, a multiplicative decomposition of the deformation gradient into a mechanical and a thermal part has been applied. The Von Mises J 2 plasticity with isotropic hardening criterion has been selected for the solid-phase of the model. Representative numerical examples, as well as the influence of single material parameters on the model will be shown. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 9
    Publication Date: 2013-11-30
    Description: Within measurements of brake pads on the IDS high load Tribometer, the wear of pads was investigated by a new non-contact wear measurement under low normal pressures and low temperatures. The first results show that the wear of the pad in the sliding friction is nearly proportional to the friction work, and inversely proportional to the shear strength. The results are also interpreted by the adhesion theory of friction and Archard's equation. On the basis of further interpretations of shear strength and extension of adhesion theory of friction, the wear is derived as a piecewise linear function, which can evaluate explicitly the effect factors of wear and relative correlations at different pressures and different temperatures. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 10
    Publication Date: 2013-11-30
    Description: The modeling of size effects in elastic-plastic solids, such as the width of shear bands or the grain size dependence in polycrystals, must be based on non-standard theories which incorporate length-scales. This is achieved by models of strain gradient plasticity , incorporating spatial gradients of selected micro-structural fields which describe the evolving dissipative mechanisms. The key aspect of this work is to provide a rigorous incremental variational formulation and mixed finite element design of additive finite gradient plasticity in the logarithmic strain space. We start from a mixed saddle point principle for metric-type plasticity, which is specified for the important model problem of isochoric plasticity with gradient-extended hardening/softening response. To this end, we propose a novel finite element design of the coupled problem incorporating a local-global solution strategy of short- and long-range fields. This includes several new aspects, such as extended Q1P0-type and MINI-type finite elements for gradient plasticity [4]. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 11
    Publication Date: 2013-11-30
    Description: A one-dimensional strain gradient plasticity model is reviewed in the context of Finite Element Method (FEM) solvability. It is found that under certain conditions specified the resulting system of two coupled partial differential equations in space and time leads to a symmetric global stiffness matrix. This is achieved upon standard weak form approach and yields a favorable system for an efficient numerical solution. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 12
    Publication Date: 2013-11-30
    Description: The deformation in polycrystals is often heterogenous, e.g. due to grain size dependent hardening. In a semi-analytical representative volume element (RVE), a log-normal distributed grain size is assumed together with a grain size dependent local plastic behavior. The numerical results are well approximated by a simple analytical expression. The effect of the homogenization comparison stiffness on the transient behaviour is explained using a simplified localization equation. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 13
    Publication Date: 2013-11-30
    Description: In this paper, we present a constitutive model for granular materials exhibiting microstructures using the concept of energy relaxation. Within the framework of Cosserat continuum theory the free energy of the material is enriched with an interaction energy potential taking into account the counter rotations of the particles. The enhanced energy potential fails to be quasiconvex. Energy relaxation theory is employed to compute the relaxed energy which yields all possible displacement and micro-rotations field fluctuations as minimizers. Based on a two-field variational principle the constitutive response of the material is derived. The developed constitutive model is then implemented in a finite element analysis program using the finite element method. Numerical simulations are presented to observe the localized deformation phenomenon in a granular medium. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 14
    Publication Date: 2013-11-30
    Description: In nowadays polymer materials are used in a multitude of different applications. A promising class of smart materials are biodegradable polymers. The present work proposes a micromechanical motivated description of degradation. Since degradation leads finally to an eroding material both cases of erosion, namely bulk and surface erosion, are considered. Degradation is modelled in a strong coupled chemo mechanical framework for an arbitrary spatial motion problem. Deformations arising due to surface erosion are described as material motion. Finally, the modelling concept is embedded in a finite element method. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 15
    Publication Date: 2013-11-30
    Description: For the simulation of the interaction of elastic waves in CFRP plates with inhomogeneities and defects the spectral finite element method (SEM) is under investigation. The SEM uses high-order shape functions which are composed of Lagrange polynomials with nodes at the Gauss-Lobatto quadrature (GLq) points. In this way we obtain a diagonal mass matrix which makes an explicit time scheme more efficient. The goal of this work is to investigate the effect of SEM on the CFL-Condition. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 16
    Publication Date: 2013-11-30
    Description: In this paper, composite structures are considered which consist of several layers of carbon fiber reinforced plastics (CFRP). For such layered composite structures, delamination constitutes one of the major failure modes and hence predicting its initiation is essential for their design. Evaluating stress-strength relation based onset criteria requires an accurate representation of the through-the-thickness stress distribution, which can be particularly delicate in the case of shell-like structures. Thus, in this paper, a solid-shell finite element is utilized, which allows for incorporating a fully three-dimensional material model, still being suited for application to thin structures. Moreover, locking phenomena are cured by using both the EAS and the ANS concept, and numerical efficiency is ensured through reduced integration. The proposed anisotropic material model accounts for the material's micro-structure by using the concept of structural tensors. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 17
    Publication Date: 2013-11-30
    Description: In this contribution, a micromechanical modeling approach in the framework of poromechanics is adopted to study structure-stiffness relations of two quite different species, namely spruce and yew, in detail. In particular, microstructural specialties of yew and spruce are assessed. A dominant influence of the cellulose content and its orientation on the stiffness of the cell wall is revealed, while on the macroscopic scale, density is found to be the governing microstructural characteristic for elastic properties. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 18
    Publication Date: 2013-11-30
    Description: PDE-constrained parameter optimization problems suffer from the high dimensionality of the corresponding discretizations, which results in long optimization runtimes. One possible approach to solve such large scale optimization problems more rapidly is to replace the PDE constraint by a low-dimensional model constraint obtained via model reduction. We present a general technique for certification of such surrogate optimization results by a-posteriori error estimation based on Reduced Basis (RB) models. We allow arbitrary PDEs and optimization functionals, in particular cover nonlinear optimization problems. Experiments on a stationary heat-conduction problem demonstrate the applicability of the error bound. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 19
    Publication Date: 2013-11-30
    Description: In a number of fcc materials such as copper or aluminum, as well as more complex materials such as twinning induced plasticity (TWIP) steels, the interaction between dislocations and other defects such as stacking faults or twins plays an important role in the hardening behavior of such materials. Interactions of dislocation and twin or stacking fault layers have been studied in this work using molecular dynamics. Depending on the material and the loading conditions, possible interaction modes include (i) penetration of the dislocation into the faulted layer, (ii) reduction of the faulted layer after interaction, (iii) growth of the faulted layer after interaction. Such studies up to this point have been performed without temperature control near zero K (0 to 2 K). In this work, we extend the previous studies to higher temperature with the help of two methods, both based on molecular dynamics (MD) modeling. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 20
    Publication Date: 2013-11-30
    Description: The paper reports on Direct Numerical Simulations of bubble-laden flows performed to investigate the interaction of bubbles with turbulence in an upward flow between two parallel vertical plates. Two simulations are presented with uniform bubble diameter and a third one with bi-disperse bubbles. Three different approaches are used to characterize bubble clustering in the investigated configuration. Horizontal pairing and tendency to form cluster has been found for all reported cases, slightly less pronounced in the bi-disperse swarm. Among other results, a 60°-alignment has been found by means of the angular pair correlation function for the mixed pairs in the bi-disperse swarm. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 21
    Publication Date: 2013-11-30
    Description: During wheel bumping caused by stochastic road excitation, the wheel performs rotational and translational movements. The bump and rebound wheel velocity leads to significant angular velocities based on the (elasto-)kinematics of the suspension system. Based on the gyroscopic effect, moments arise about the rotating wheel induced by the angular change while bumping. Therefore it leads to undesirable wheel changes and degrades the tire contact and finally decreases the driving stability. A flexible MBS-model of the five-link rear axle system that includes these effects has been built up to allow a detailed investigation of the gyroscopic effect. Using the simulation results, conclusions can be drawn for refining design criteria for the kinematics, elastokinematics and topology of the suspension system to increase the active safety of the vehicle. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 22
    Publication Date: 2013-11-30
    Description: Dynamics of multi deformable bodies coupled by standard light fractional order discrete continuum layers is described by coupled partial fractional order differential equations. A mathematical analogy and phenomenological mapping between generalized coordinates of fractional order discrete chain systems and eigen time functions correspond to one of infinite numbers of eigen amplitude functions of dynamics of multi deformable bodies (beams, plates or membranes) coupled by standard light fractional order discrete continuum layers are identified. Eigen fractional order vibration modes are approximately determined analytically and graphically presented. A number of theorems is defined and proofed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 23
    Publication Date: 2013-11-30
    Description: A viscoplastic strain gradient crystal plasticity theory based on the gradient of the equivalent plastic strain ∇γ eq is proposed. A grain boundary yield condition is introduced. The microstructural explanation of the Hall-Petch effect, accounting for notch-like stress concentrations at the grain boundary as a result of discrete slip bands, is reviewed. Periodic tensile test FEM simulation results illustrate the prediction of the numerical model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 24
    Publication Date: 2013-11-30
    Description: Volume 13 (2013) of PAMM “Proceedings in Applied Mathematics and Mechanics” assembles the contributions to the 84th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik, held 18 – 22 March 2013 at the University of Novi Sad, Serbia. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections Minisymposia Mathematics Ma 1 Model reduction for PDEs Minisymposia Mechanics Me 1 Nano-mechanics of carbon nanoparticles Me 2 Size-dependent crystal plasticity: experiment, theory and simulation Me 3 Simulation and modeling of bubbly flows Sections 1–24 1 Multi-body dynamics 2 Biomechanics 3 Damage and fracture mechanics 4 Structural mechanics 5 Nonlinear oscillations 6 Material modelling in solid mechanics 7 Coupled problems 8 Multiscales and homogenization 9 Laminar flows and transition 10 Turbulence and reactive flows 11 Interfacial flows 12 Waves and acoustics 13 Flow control 14 Applied analysis 15 Applied stochastics 16 Optimization 17 Applied and numerical linear algebra 18 Numerical methods of differential equations 19 Optimization of differential equations 20 Dynamics and control 21 Mathematical image processing 22 Scientific computing 23 Applied operator theory Young Researchers' Minisymposia YR Ma2 Analytical and engineering aspects in the material modeling of solids YR Ma3 Numerical methods with non-matching meshes YR Me2 Scale-bridging modeling and simulation – methodological and computational aspects YR Me3 Isogeometric methods
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  • 25
    Publication Date: 2013-11-30
    Description: Articular cartilage is a multiphase material consisting of fluids and electrolytes, which is described with the Theory of Porous Media. The mechanical characteristics of articular cartilage are porosity, incompressible material behavior combined with transversely isotropic behavior for solid and fluid phases. There are two central points to model articular cartilage: the poro-viscosity of the porous matrix and the visco elasticity, and orientation of the collagen fibers. A numerical example is presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 26
    Publication Date: 2013-11-30
    Description: Orientation of collagen fibers and their spatial distribution predefine macroscopic mechanical properties of the soft tissue and in particular its anisotropy directions. In this contribution, we apply two different procedures to automatically generate these directions for a 3D FE-model. The first procedure is based on an analogy with a heat conduction problem. Accordingly, a thermal flux under certain temperature boundary conditions is calculated by the same FE model and is further utilized for the definition of the anisotropy directions. The numerical result shows good agreement with Langer's lines data in human skin. Within the second procedure, the fiber vector field is calculated by the Laplacian smoothing method based on the user defined fiber direction sketches. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 27
    Publication Date: 2013-11-30
    Description: The current paper proposes a model for describing mechanical phenomena that occur during the process of mammal fertilization when spermatozoa impact the surface of Zona Pellucida. Zona pellucida (ZP) is a dynamical 3D matrix that surrounds the mammalian oocyte. In the process of fertilization, sperm cell has to penetrate this structure. To describe impact of sperm cells with velocities that are effective and those that are ineffective relative to the oscillatory behavior of ZP , the discreet continuum model in the form of spherical net model is used. Resultant trajectories of knot mass particles dynamics of mouse ZP spherical net model in the form of generalized Lussajous curves are presented. Using generalized Lussajous curves, parametric frequency analysis of oscillatory behavior of knot material particles in the mouse ZP spherical net model is conducted. The influence of impact angles of sperm cells on corresponding knot mass particle trajectory is discussed. Favorable and unfavorable trajectories of knot mass particle motions are discussed in the context of successful fertilization. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 28
    Publication Date: 2013-11-30
    Description: Multi body system contains finite number of rigid bodies that are placed on each axis, which do not intersect each other. Derivatives of the linear momentum and angular momentum with respect to time by use mass moment vectors and vector rotators for pole and axis, are determined. A number of theorems are defined. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 29
    Publication Date: 2013-11-30
    Description: In the present work the mechanical behaviour of a dual-rotor vibrotactor has been investigated with special attention to its stationary motions and their linear stability. After the introduction of the used mechanical model, the formulae for the stationary motions are given, and characteristic stablity charts are presented. The linear stability is investigated for uncontrolled and controlled system as well. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 30
    Publication Date: 2013-11-30
    Description: This work is devoted to parametric study on creep-fatigue endurance of the steel AISI type 316N(L) weldments defined as type 3 according to R5 Vol. 2/3 procedure at 550°C. The study is implemented using a novel direct method known as the Linear Matching Method (LMM) and based upon the creep-fatigue evaluation procedure considering time fraction rule for creep-damage assessment. Seven geometrical configurations of the weldment, which are characterised by individual values of a geometrical parameter ρ, are proposed. Parameter ρ, which represents different grades of TIG dressing, is a ratio between the radius of the fillet of the remelted metal on a weld toe and the thickness of welded plates. For each configuration, the total number of cycles to failure N * in creep-fatigue conditions is assessed numerically for different loading cases including normalised bending moment and dwell period Δ t . The obtained set of N * is extrapolated by the analytic function dependent on , Δ t and ρ. Proposed function for N * shows good agreement with numerical results obtained by the LMM. It is used for the identification of Fatigue Strength Reduction Factors (FSRFs) effected by creep and dependent on Δ t and ρ. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 31
    Publication Date: 2013-11-30
    Description: We introduce a consistent variational framework for inelasticity at finite strains, yielding dual balances in physical and material space as the Euler equations. The formulation is employed for the simultaneous usage of configurational forces as both driving forces for crack propagation as well as h -adaptive mesh refinement. The theoretical basis builds upon a global balance of internal and external power, where the mechanical response is exclusively governed by two scalar functions, the free energy function and a dissipation potential . The resulting variational structure is exploited in the context of fracture mechanics and yields evolution equations for internal variables. In the discrete setting, we present a geometry model fully separated from the finite element mesh structure that represents structural changes of the material configuration due to crack propagation. Advanced meshing algorithms provide an optimal discretization at the crack tip. Local and global criteria are obtained via error estimators based on configurational forces being interpreted as indicators of an energetic misfit due to an insufficient discretization. The numerical handling is decomposed into a staggered algorithm scheme for the dual set of equilibrium equations in material and physical space and efficient mesh generation tools. Exemplary numerical examples are considered to illustrate the method and to underline the effects of inelastic material behaviour in the presented context. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 32
    Publication Date: 2013-11-30
    Description: The contribution adresses the simulation of ferroelectric matrials in the framework of the Piezoresponse Force Microscopy (PFM). Based on the PFM, ferroelectric domain structures can be analyzed in great detail by measuring the electrically induced mechanical deformations of the surface of a ferroelectric. We employ a flexible continuum-mechanical model based on the phase-field method in order to analyze the behavior of ferroelectric microstructures numerically. Since ferroelectric materials are often highly anisotropic, the phase-field formulation will account for transversely isotropic symmetry. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 33
    Publication Date: 2013-11-30
    Description: The present contribution deals with the atomistic modelling of ferroelectric barium titanate. In this context a core-shell model is implemented in a Molecular Static algorithm. Furthermore, Coulomb forces are simulated by the Wolf summation method in order to allow for a small cut off radius. We discuss the core-shell model, molecular statics as a finite elements approach and present some numerical results. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 34
    Publication Date: 2013-11-30
    Description: This work is concerned with the material modeling of the inelastic behavior of bonding and debonding effects in adhesive layers. High-strength adhesives are applied in building industries utilizing thick adhesive layers due to huge building elements and construction tolerances. Therefore a continuum approach is presented to describe the nonlinear material behavior. In the failure criterion two stress invariants are used, which involves the hydrostatic pressure as well as the deviator stress state. A non-associated flowrule, which determines the evolution of the inelastic variables, is required to ensure the thermodynamical consistency of the model. Hardening and softening are included as well as the rate-dependency of the adhesive. Furthermore the viscoplastic approach is used for regularization of the mesh dependency in case of material softening. The nonlinear material model is implemented in a finite element program. The material tangent modulus is incorporated to obtain quadratic convergence for the global equilibrium iteration. The identification of material parameters is discussed on the simulation of typical experiments for adhesive materials. As a drawback of the presented phenomenological material model, the large number of parameters involved in the constitutive description is discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 35
    Publication Date: 2013-11-30
    Description: In this work a material model for shape memory alloy (SMA) fibers is presented. A constitutive model is provided which aims for computational use. The presented model incorporates all relevant material nonlinear phenomena. It takes pseudoplasticity into account as well as pseudoelasticity and further the shape memory effect (SME). The constrained SME (CSME) and the two-way SME are covered by the presented material model. The constitutive model is implemented in a one-dimensional truss formulation and in a 3D-rebar element. Both formulations are used to model fiber composite structures. Those are described by the use of a non-conforming and a conforming mesh on the mesoscale. The numerical examples show the capability of the formulation. Different meshing strategies for the fiber–matrix compound are discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 36
    Publication Date: 2013-11-30
    Description: From a macroscopic point of view, the deformation of most metals results in an evolution of the symmetry groups characterizing the isotropy of the considered materials. With respect to plastic deformation for instance, the shape of the macroscopic yield surface evolves during deformation. In the present paper, a novel constitutive framework capturing this evolution is proposed. This framework is based on the fundamentals of thermodynamics. Furthermore, it also shows a variational structure such that all state variables follow jointly from minimizing an incrementally defined energy functional. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 37
    Publication Date: 2013-11-30
    Description: There exists a large variety of different techniques used to generalize the Prandtl-Reuss relations of small strain elasto-plasticity to finite strains. Obviously, any systematic study of such generalization techniques should be based on some sound principles. In this work, one aspect is taken into account, concerning arbitrary isochoric change of the local reference configuration. We analyze some models of finite strain elasto-plasticity in order to find out if the specific choice of the reference configuration can affect the predicted stress response. For material models which remain invariant under the reference change, no preferred reference configuration exists. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 38
    Publication Date: 2013-11-30
    Description: Quasi-static cyclic loading tests on filled rubber-like materials reveal a significant stress softening in the first cycle. The magnitude of this softening, widely known as the Mullins effect, reduces in the next cycles until it reaches a stabilized value referred to as hysteresis. In this contribution, we associate the hysteresis with the fracture of carbon bonds in the filler network. In order to calculate the cyclic energy dissipation, we modify the classic concept of network decomposition [1, 2] and add a new network considered to be responsible for the breakage and re-formation of carbon black aggregates during loading and unloading. The proposed model is in-line with a wide range of experimental observations. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 39
    Publication Date: 2013-01-03
    Description: In this paper the linear theory of viscoelasticity for Kelvin-Voigt materials with voids is considered. The uniqueness and existence theorems for internal boundary value problem (BVP) of steady vibrations are proved by means of the potential method (boundary integral method) and the theory of singular integral equations. The application of this method to the 3D BVP of the considered theory reduces this problem to 2D singular integral equation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 40
    Publication Date: 2013-11-30
    Description: A flow structure interaction of a membrane and a fluid is investigated. A conventional segregated numerical algorithm, where the membrane deformation and the flow dynamics are calculated alternately has to fail due to the artificial added mass instability. Thus, a new iteration scheme is proposed. In order to get a good prediction for the deformation of the membrane, the equations describing the membrane are coupled to a potential flow solver (panel method). Then a CFD solver can be used to determine the corrections of the flow field due viscosity and turbulence. An example is presented that this procedure seems to be numerically stable. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 41
    Publication Date: 2013-11-30
    Description: A multivariant phase field model for martensitic transformations in elastoplastic materials is introduced which is in mathematical terms the regularization of a sharp interface approach. The evolution of microstructure is assumed to follow a time dependent Ginzburg-Landau equation. The coupled problem of the mechanical balance equation and the evolution equations is solved using finite elements and an implicit time integration scheme. In this work, plasticity is considered for the austenitic phase which influences the martensitic evolution. With aid of the model these interactions are studied in detail. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 42
    Publication Date: 2013-11-30
    Description: We discuss generalized boundary conditions for representative volume elements (RVE), which include the classical boundary conditions as special cases. From the generalization, stochastic boundary conditions are derived. These allows to adjust the the stiffness of the boundary conditions smoothly between the extremal cases of homogeneous strain and homogeneous stress boundary conditions. We found that it needs to be distinguished between the resistance of the boundary conditions against homogeneous and inhomogeneous RVE deformation. The stochastic BC can combine the moderate stiffness of the well known periodic boundary conditions with the high resistance against localization of the homogeneous strain boundary conditions. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 43
    Publication Date: 2013-11-30
    Description: In the present contribution, the problem of non-linear deformation of materials with stochastically distributed anisotropic inclusions is considered on the basis of the methods of mechanics of stochastically non-homogeneous media. The homogenization model of materials of stochastic structure with physically non-linear components is developed for the case of a matrix which is strengthened by unidirectional ellipsoidal inclusions. It is assumed that the matrix is isotropic, deforms non-linearly; inclusions are linear-elastic and have transversally-isotropic symmetry of physical and mechanical properties. Stochastic differential equations of physically non-linear elasticity theory form the underlying equations. Transformation of these equations into integral equations by using the Green's function and application of the method of conditional moments allow us to reduce the problem to a system of non-linear algebraic equations. This system of non-linear algebraic equations is solved by the Newton-Raphson method. On the analytical as well as the numerical basis, the algorithm for determination of the non-linear effective characteristics of such a material is introduced. The non-linear behavior of such a material is caused by the non-linear matrix deformations. On the basis of the numerical solution, the dependences of homogenized Poisson's coefficients on macro-strains and the non-linear stress-strain diagrams for a material with randomly distributed unidirectional ellipsoidal pores are predicted and discussed for different volume fractions of pores. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 44
    Publication Date: 2013-11-30
    Description: In this paper, we present a numerical procedure that can be used to model the electro-mechanical coupled behavior of the dielectric actuator domain. The equation describing the electrostatical part is given by the reduced form of the Maxwell equation and the electrostatic potential [1]. The mechanical problem is described by the constitutive equations and equilibrium equations. Using the finite element method, this technique is to divide a whole problem into sub-problems. The complexity of the original problem is therefore reduced by focusing only on the most relevant areas. A finite element analysis is then performed by applying the electrostatic Maxwell pressure as Neumann boundary conditions to compute the displacements. Once the displacement is computed, the electrostatic domain or the conductor is updated. Electrostatic analysis is performed on the updated geometry and the finite element method is then used to determine the change in potential due to geometric perturbations. Once the surface charge densities are known, the new electrostatic Maxwell pressure is computed. The mechanical and electrostatic analysis is repeated until an equilibrium state is computed. The procedure is demonstrated in the paper by the solution of some two-dimensional and three-dimensional problems. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 45
    Publication Date: 2013-11-30
    Description: In this work a comparison of polycrystal and classical continuum models illustrated by examples of full structures is investigated. The general idea is to represent the averaged distribution of displacement, stress and strain fields for statistically randomized realizations of discrete structures. A technique for averaging fields in the FEM program ABAQUS is proposed and implemented. To improve the computation efficiency mesh dependence was investigated. Results of simulation are given for a rectangular plate and for the Kirsch's problem for both examples elastic as well as inelastic material behavior. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 46
    Publication Date: 2013-11-30
    Description: This paper presents a quasi-static solution for the mechanically coupled diffusion problem in a Lithium-ion battery thin film electrode during charge. The concentration field and the stresses are calculated under the assumption of a constant flux. The influence of the electrode's stiffness, its thickness, and of the current density on the results are discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 47
    Publication Date: 2013-11-30
    Description: The reformulation in conservative form of the higher-dimensional continuum dislocations dynamics(hdCDD) theory of Hochrainer (Ph.D. thesis, 2006) is presented together with a framework for elasto-plasticity problem based on this theory. A Runge-Kutta discontinuous Galerkin(RKDG) method is used for the evolution of hdCDD to obtain information of the micro-structure which is coupled with a finite element method for the stress computation. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 48
    Publication Date: 2013-11-30
    Description: In this work, we analyze a strategy for the selection of the adequate RVE size for elastic problems on thin sheets with strong texture. The selection strategy includes the construction of the geometric descriptor as periodic tesselation of the sheets and the stochastic assignment of stiffness matrices for the different material grains inside the RVE. The procedure is illustrated with an example on DC01 steel sheets with thickness 50 µm. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 49
    Publication Date: 2013-11-30
    Description: The motion and interaction of dislocation lines are the physical basis of the plastic deformation of metals. Although ‘discrete dislocation dynamic’ (DDD) simulations are able to predict the kinematics of dislocation microstructure (i.e. the motion of dislocations in a given velocity field) and therefore the plastic behavior of crystals in small length scales, the computational cost makes DDD less feasible for systems larger than a few micro meters. To overcome this problem, the Continuum Dislocation Dynamics (CDD) theory was developed. CDD describes the kinematics of dislocation microstructure based on statistical averages of internal properties of dislocation systems. In this paper we present a crystal plasticity framework based on the CDD theory. It consists of two separate parts: a classical 3D elastic boundary value problem and the evolution of dislocation microstructure within slip planes according to the CDD constitutional equations. We demonstrate the evolution of dislocation density in a micropillar with a single slip plane. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 50
    Publication Date: 2013-11-30
    Description: In this work, a micromechanically motivated affine full network model (AFNM) is used to simulate the load-displacement response of nonwoven materials. These materials are made from synthetic advanced fibers by bonding or interlocking networks of randomly laid fibers through mechanical, chemical or thermal processes. This results into a random fibrous network microstructure and a highly inhomogeneous response to external loadings with a very high degree of anisotropy. The load-displacement response under large strains is observed to be highly non-linear with a stiffening behavior which is also accompanied by complex dissipative phenomena. The preliminary simulation results with the AFNM, after reducing to two-dimensional setting, highlight its limitations and help identify the areas of improvement for a realistic material modeling. Reorientation of fibers are shown to play a critical role in the overall macroscale response of the materials. A new evolution law for reorientation is presented in the form of a first order ordinary differential equation where an exact analytical solution to the same is also computed. Improvements of the predicted load-displacement response signify the microscopic origins of the non-linear stiffening behavior as reorientation of fibers. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 51
    Publication Date: 2013-11-30
    Description: The finite cell method is extended to enable the computation of solids consisting of heterogeneous materials. The approach is based on a domain decomposition utilizing the hp-d method. Our results reveal that the proposed method improves the accuracy of the finite cell method significantly. It also paves the way for combining the finite cell method with other approaches like partition of unity based methods which can be of interest in many cases, such as dealing with composites and numerical homogenization. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 52
    Publication Date: 2013-11-30
    Description: The focus of this paper is on the simulation of two-phase magneto-electric (ME) composites, consisting of a piezoelectric matrix with piezomagnetic inclusions. In such composites, the coupling between electric and magnetic fields is strain-induced and thus ME coupling arises as a product porperty. In order to compute the effective properties of the composite a computational homogenization scheme based on the Finite Element Method will be applied. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 53
    Publication Date: 2013-11-30
    Description: The mechanical vibrations have been perceived as unhealthy, although in some circunstances these may lead to a human body fortification. The trainings that use the vibrating stimulus have certain advantages to the classical trainings. Stabilizers and postural muscles are less visible, being hidden by large muscle groups and have little growth potential. For this reason most types of training does not focus on training and strengthening them. This article presents the advantages of training muscular groups of the vertebral column performed on vibrating plates. This type of training has the advantage that besides the requiring to all muscles in where the vibratory stimulus reaches, leads to an increase flexibility of joints. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 54
    Publication Date: 2013-11-30
    Description: The authors of this paper aim to highlight issues related to the organology and the integration of the hardware component in the mechanical structure of a tracked mini robot, called Robo Geniu , part of the unmanned ground vehicles category having the ability to act autonomously and enabling its endowment with means of observation, listening, tapping, relaying and jamming. This paper reveals, in detail, the composing parts of the hardware component, as well as the way they are assembled in the mechanical structure of the mini robot under study. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 55
    Publication Date: 2013-11-30
    Description: Computational expenses restrict the usage of continuum mechanics in modelling (parts of) the musculoskeletal system, although, continuum mechanics would provide the possibility to represent the complex mechanical behaviour of a muscle-tendon complex (MTC). This work provides an overview on a modelling framework, which aims to achieve forward-dynamics simulations of musculoskeletal systems by coupling three-dimensional continuum-mechanical-based finite element simulations to rigid-body simulations based on a simplified two-muscle upper arm model. Here, the focus is on implementing a sophisticated representation of the skeletal MTC and tissue-bone interaction. The three-dimensional continuum-mechanical description of the skeletal muscle is described within the framework of finite elasticity. To model the MTC, two additional parameters are introduced providing the possibility to describe muscle tissue, tendon tissue, and soft tissue within one set of constitutive equations. Further, a realistic fibre orientation for the skeletal muscles and contact mechanics between the muscles and the bones is considered. For different elbow flexion angle positions, the muscles' mechanical state is compared with and without considering contact mechanics. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 56
    Publication Date: 2013-11-30
    Description: Two approaches of including active contractile behaviour of muscle tissue written in a continuum-mechanical formulation are presented. One approach relies on the addition of active and passive stress contributions, while the other approach is based on a multiplicative decomposition of the deformation gradient tensor. Both formulations can be stated in a thermodynamically consistent manner, each with different constraints, and both models can reproduce experimental data of passive and fully active muscle. Different behaviours are observed when comparing the active muscle models at submaximal stimulation rates. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 57
    Publication Date: 2013-11-30
    Description: The reinforcement of porous vertebral cancellous bone by the injection of bone cement is a practical procedure for the stabilisation of osteoporotic compression fractures and other weakening lesions. This contribution concerns the reproduction and prediction of the resulting bone-cement distribution during the injection procedure by means of numerical simulation. A detailed micromechanical (locally single-phasic) model exhibits the drawback that all geometrical and physical transition conditions of the individual parts of the complex aggregate have to be known. Therefore, we rather proceed from a macroscopic (and multi-constituent) continuum-mechanical model based on the Theory of Porous Media. In this regard, the homogenisation of the underlying micro-structure results in a model of three constituents: these are the solid bone skeleton, which is saturated by the liquid bone marrow that may be displaced by the injected liquid bone cement. The influence of the micro-architecture of the pore space on the spreading of the bone cement is considered by a spatial diversification of the anisotropic permeability tensors, obtained through image processing techniques applied to medical imaging data (µCT). The numerical investigation of the strongly coupled problem enables the study of vertebroplasty and allows for the comparison between the simulation results and the experimentally determined bone-cement distribution that were imaged during injections. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 58
    Publication Date: 2013-11-30
    Description: In this contribution we investigate the influence of dispersed microscopic quantities on the damage behavior in collagenous tissues. Therefore, we derive a damage model, that may take into account statistical distributions of collagen fiber properties. In detail, we regard distributions of the orientation of fibril-interconnecting proteoglycan (PG) bridges and of an internal fibril length parameter. The damage model is embedded into the constitutive framework from [1] and a numerical example in a finite element framework is given. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 59
    Publication Date: 2013-11-30
    Description: The presented continuum mechanical model describes isotropic and transversely isotropic growth in biphasic materials with focus on biological tissue. The model is capable to describe full isotropic growth, full transversely isotropic growth as well as a combination of both types. This approach is chosen to describe the most common occurring growth types, namely isotropic and transversely isotropic growth, but also to describe effects where the growth of the investigated body depends on multiple single growth effects that are difficult to distinguish among each other. For the description of growth a biphasic homogenized approach within the framework of the theory of porous media (TPM) is used. In this work we focus on the applied formulation of multiple multiplicative decoupling of the deformation gradient into elastic, growth, isotropic and transversely isotropic parts including the governing constitutive equations. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 60
    Publication Date: 2013-11-30
    Description: This work presents an extension of newly developed 3D finite elements to model failure in purely mechanical based materials [1, 2] to electromechanical coupled materials. Following the approach suggested in [6] for the plane setting, new finite elements are developed, which in addition to resolving strong discontinuities in the mechanical displacement field are capable of modeling strong discontinuities in 3D also in the electric potential. An application to a 3D off-centered three point bending test under combined mechanical and electrical loading outlines the performance of the newly developed finite elements. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 61
    Publication Date: 2013-11-30
    Description: A simulation model for damage evolution in slip bands under VHCF condition is presented. By use of a numerical method it is applied to a real simulated microstructure of AISI304. It considers orientations of slip systems as well as individual anisotropic elastic properties in each grain. The numerical method is the two-dimensional boundary element method which is based on two integral equations and implies fundamental solutions for anisotropic elastic solids. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 62
    Publication Date: 2013-11-30
    Description: In phase field fracture models cracks are indicated by the value of a scalar field variable which interpolates smoothly between broken and undamaged material. The evolution equation for this crack field is coupled to the mechanical field equations in order to model the mutual interaction between the crack evolution and mechanical quantities. In finite element simulations of crack growth at comparatively slow loading velocities, a quasi-static phase field model yields reasonable results. However, the simulation of fast loading or the nucleation of new cracks challenges the limits of such a formulation. Here, the quasi-static phase field model predicts brutal crack extension with an artificially high crack speed. In this work, we analyze to which extend a dynamic formulation of the mechanical part of the phase field model can overcome this paradox created by the quasi-static formulation. In finite element simulations, the impact of the dynamic effects is studied, and differences between the crack propagation behavior of the quasi-static model and the dynamic formulation are highlighted. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 63
    Publication Date: 2013-11-30
    Description: The degeneration of articular cartilage is one of the most common causes of pain and disability in middle-aged and older people. In this context, osteoarthritis is a well-known clinical syndrome related to cartilage degeneration. The degeneration of normal articular cartilage is not simply the result of aging and mechanical wear. Pathological loads may also increase the risk of degeneration of normal joints, and individuals who have an abnormal joint anatomy or inadequate muscle strength probably have a greater risk of degenerative joint disease. The goal of this contribution is to investigate the influence of cartilage degeneration on the stress pattern at the cartilage-bone interface. In this connection, articular cartilage is described as a highly anisotropic and heterogeneous charged biphasic solid-fluid aggregate in the framework of the Theory of Porous Media (TPM). After calibration of the model under physiological loading conditions, the results of a sensitivity analysis of the model parameters are presented. Realistic boundary conditions are applied on the cartilage surface of the femoral head obtained from multibody dynamics calculations. Use is made of the Hertzian contact theory for the contact pressure distribution. The applicability of a new rendition technique to visualise simulation results based on a standardised stereographic projection of the von Mises stresses along the curved cartilage-bone interface is introduced. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 64
    Publication Date: 2013-11-30
    Description: The dynamics of tribological systems with pronounced memory effects are characterized by the complex coupling of mechanical, thermal, and chemical processes. At the Institute of Dynamics and Vibrations in Braunschweig, Cellular Automata have been developed that facilitate the evaluation of dynamics in technically relevant systems within a reasonable time. The flow of wear material is decisive for the formation, localization, and reconstitution of load-bearing structures or films. In this paper, two opposed frictional contacts are chosen exemplarily for the investigation of the wear particle flow: a vehicle brake system and the sanding of wood. For this purpose, a modeling technique is proposed that is based on established force laws for micro particles and differentiates mechanisms of transport for different phases of the particle movement. The resulting transport of a single particle interacting with the topology of the frictional gap is analyzed for varying particle properties and process parameters. In a second step the insights are transferred to a set of rules for a Cellular Automaton which allows for quick evaluation and the incorporation of coupled effects. The validity and quality of the model transfer are discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 65
    Publication Date: 2013-11-30
    Description: Die Beweglichkeit von Wasserrinnsalen auf Zylinderoberflächen besitzt beim hydroaeroelastischen Phänomen der Regen-Wind induzierten Schwingungen, welches bei geneigten Kabeln und Hängern von Schrägkabelbrücken und Bogenbrücken durch gleichzeitiges Auftreten von Regen und Wind entstehen kann, eine elementare Bedeutung für den Erregermechanismus [1]. Bei der Untersuchung des Schwingungsphänomens ist bei der Modellierung der Rinnsale neben der Beschreibung ihrer Beweglichkeit auch die genaue Kenntnis ihrer Gleichgewichtslagen auf der Zylinderoberfläche wichtig. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 66
    Publication Date: 2013-11-30
    Description: New structures become larger, lighter, and slender in practical applications. The problem of large elastic deformations undergoing overall motion in these structures has to be considered in the dynamic modeling. Using descriptions considering the nonlinear strain displacement relationships, the couplings between overall motions and the flexible deformations can be taken into account. Several approaches exist in the literature, but are not compared. These models are briefly introduced and explained with respect to the above mentioned problem. Effects of different couplings of different order combining nonlinear kinematics and higher order kinetics of flexible deformations are therfore investigated systematically. The results allow a deep insight and therfore understanding of related effects. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 67
    Publication Date: 2013-11-30
    Description: This paper communicates a new algorithmic concept, how higher-order Runge-Kutta (RK) methods for time integration of viscoelastic constitutive laws can be introduced into nonlinear finite element methods in order (i) to obtain the full nominal order p in time integration, (ii) to ensure that global equilibrium is only required at the end of time intervals Δ t but not in the interior at RK-stages, and (iii) to obtain –based on (i) and (ii)– a considerable speed-up compared with Backward-Euler. The condition to realize (i)–(iii) is, that the approximation of total strain in time must be of the same order as the time-integration method, which is a completion of the concept of algorithmic consistency in computational inelasticity. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 68
    Publication Date: 2013-11-30
    Description: In order to solve the so-called consistently linearized eigenproblem in the frame of the Finite Element Method (FEM), the derivative of the tangent stiffness matrix with respect to the load parameter λ needs to be calculated. In this work, three schemes for calculation of are presented. The first scheme is based on an analytical expression for the first derivative of e the element tangent stiffness matrix with respect to λ for the special case of a co-rotational beam element. The second one is a finite difference approach for computation of . The third one is also a finite difference approach. However, it is based on a directional derivative of . An elastic beam, subjected to a compressive axial force and a small transverse uniform load, is chosen as a numerical example. The effectiveness and the accuracy of the three schemes are compared. The third scheme is found to be not only very practical but also more effective than the two competing schemes. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 69
    Publication Date: 2013-11-30
    Description: Large strain magneto-viscoelastic deformations in the presence of a finite magnetic field are modelled in this paper. Internal dissipation mechanisms are proposed using a multiplicative decomposition of the deformation gradient and an additive decomposition of the magnetic induction. Using thermodynamically consistent constitutive and evolution laws, numerical results showing stress relaxation and magnetic field evolution are presented to illustrate the theory. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 70
    Publication Date: 2013-11-30
    Description: Soils consist of a porous soil skeleton filled by fluids like air and water. The accurate description of their mechanical behaviour requires a coupled solid-fluid approach. The analysis is based on a set of balance equations, kinematic equations and constitutive equations, the latter including a material model for the soil. Depending on the degree of saturation, the soil behaviour has to be modelled in both, partially and fully saturated state. We present a constitutive model for soils developed from the cap model proposed by Kohler and Hofstetter. The elasto-plastic model is formulated in terms of two independent stress variables, generalised effective stress σ ij ☆ and matric suction p c . It is applicable to partially and fully saturated state. The yield surface includes a shear failure envelope and a hardening cap surface. Its evolution in terms of matric suction is controlled by the load collapse (LC) yield curve and parameters defining the suction-dependent intersection of the shear failure envelope with the 1 ☆ - p c -plane, where 1 ☆ = tr(σ ij ☆ ). Our extension of the model includes an improved LC yield curve to enable a better representation of wetting/drying paths and to allow a smooth transition from partially to fully saturated state. Numerical results for a low to medium plasticity clay are in good agreement with experimental data. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 71
    Publication Date: 2013-11-30
    Description: The prediction and simulation of material behavior by finite element methods has become indispensable. Furthermore, various phenomena in forming processes lead to highly differing results. In this work, we have investigated the process chain on a cross-shaped cup in cooperation between the Institute of Applied Mechanics (IFAM) of the RWTH Aachen and the Institute of Forming Technology and Lightweight Construction (IUL) of the TU Dortmund. A viscoplastic material model based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity has been used [1,2]. The finite strain constitutive model combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamically consistent setting. This anisotropic viscoplastic model is based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine in the commercial finite element package LS-DYNA with the electromagnetical module. The aim of the work is to show the increasing formability of the sheet by combining quasi-static deep drawing processes with high speed electromagnetic forming. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 72
    Publication Date: 2013-11-30
    Description: Investigations into the atomistic-to-continuum coupling are recently pursued in literature. A hierarchical modelling in terms of a macroscale treated by continuum mechanics and the microscale governed by statistical mechanics may be a very fruitful combination. If the microscale is simulated with the help of molecular dynamics, the isostress-isoenthalpic ensemble as proposed by Parrinello and Rahman presents a beneficial choice. This statistical ensemble is remarkable as the equations of motion are derived from a Lagrangian. Recently, this Lagrangian was situated into a continuum mechanics setting. This paper investigates the behavior of this continuum-related Lagrangian in a kinetics-driven setting (by imposing an external stress) and a kinematics-driven setting (by imposing the shape of the molecular dynamics cell) in terms of a numerical example. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 73
    Publication Date: 2013-11-30
    Description: Many material models lead to complicated formulations of the exact consistent tangent modulus tensor and therefore its derivation and implementation might be elaborate. In this case numerical approximations of the moduli can provide an alternative in particular for scientific development purposes. Here, a robust numerical approximation of the tangent modulus tensor that can be implemented within FE-software is proposed using an innovative numerical derivative scheme. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 74
    Publication Date: 2013-11-30
    Description: Oscillatory rheometer measurements are used to determine the material parameters of a NEWTONian fluid model, which can be expressed by a linear constitutive relation. However, rheological materials, such as polymer melts, mixture of oils, or food paste, can only be modeled as non-NEWTONian fluids by using non-linear constitutive relations. Since the rheometer measures the energy loss in the induction motor due to shear loading of the viscous material, this can be used as the objective function for a regression analysis. The dissipated energy will be obtained as outlined in [1]. The goal of this work is to explain how to determine the parameters of a non-linear material model by using the energy loss that is measured in a rheometer. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 75
    Publication Date: 2013-11-30
    Description: We develop a multi-mechanism model for strainrate- and temperature-dependent asymmetric plastic material behavior accompanied by phase transformations, which are important phenomena in steel production processes. To this end the well-known Johnson-Cook model is extended by the concept of weighting functions, and it is combined with a model of tranformation-induced plasticity (TRIP) based on Leblond's approach. The bulk model is formulated within a thermodynamic framework at large strains, and it will be specialized and applied to cutting processes in steel production. In the examples parameters are identified for the material DIN 100Cr6, and we illustrate the characteristic effects of our multimechanism model, such as strain softening due to temperature, rate dependence and temperature dependence as well as the SD-effect. A finite-element simulation illustrates the different mechanisms for a cutting process. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 76
    Publication Date: 2013-11-30
    Description: In this contribution, the derivation of the energy dissipation rate in generalized visco-elastic material models with internal stress-type variables and linear evolution equations is outlined. The approximated dissipation rate is computed from a positive quadratic form of the nonlinear non-equilibrium stresses and the inverse of the consistent material tangent tensor. The presented method is used to compute the energy dissipation of visco-elastic rubber material in a large scale application of a steady state rolling tire structure. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 77
    Publication Date: 2013-11-30
    Description: In this paper we present the theoretical background and application of Finite Element algorithms for linear and nonlinear problems of multiple field coupling. They enable the prediction of the electromagnetomechanical behavior of materials and structures and supply useful tools for the optimization of multifunctional composites. First, linear three-field coupling is presented within the context of a Finite Element implementation. Then, a homogenization procedure is discussed. Finally, a micromechanical model for nonlinear ferroelectric constitutive behavior and its numerical realization are outlined. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 78
    Publication Date: 2013-11-30
    Description: We propose a canonical finite strain theory for diffusion-mechanics coupling for the intercalation induced stress generation in Li-ion electrode particles. The intrinsic coupling arises from both mechanical pressure gradient-induced diffusion of Li-ion particles and diffusion induced swelling/shrinkage leading to mechanical stresses. In addition, we extend the finite strain theory for diffusion-mechanics coupling to chemomechanical fracture of electrode particles by introducing a nonlocal crack phase field which replaces a sharp crack topology with a smooth diffuse interpolation between the intact and broken states of the material. We employ a semi-implicit Galerkin-type finite element method for the solution of resulting set of differential equations. In addition to the mechanical, chemical and crack phase field, we introduce the pressure as an independent field variable in order to reduce the smoothness requirements on the interpolation functions. We illustrate characteristic features of the proposed model by means of representative initial-boundary value problems. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 79
    Publication Date: 2013-11-30
    Description: In the long term, the only way to address the challenging task of power supply, is to make renewable energy sources economically attractive and to use them efficiently. In particular, geothermal energy is promising to take over the base load of the power supply. Nevertheless, a lot of investigations needs to be made to use the almost inexhaustible source of thermal energy in the interior of the earth effectively. Starting from the initially isothermal state, a cold fluid is injected through a borehole into a rock. By the rising pressure gradient, the fluid flows through the porous rock and escapes through another borehole. While the fluid passes the micro cracks in the hot rock, the water is heated by the rock due to the heat exchange between the constituents. This process is simulated based on the Theory of Porous Media (TPM). The presented modelling approach of the heat transport and the flow processes in a fully saturated subsurface includes two non-isothermal constituents: an elastically deformable, materially incompressible solid skeleton where thermal expansion is neglected, and a viscous, materially incompressible fluid constituent. To solve the initial-boundary-value problem, the governing primary variables of the coupled model are spatially approximated by mixed finite elements, and the time-discretisation is carried out by an implicit Euler time-integration scheme. The aim of the presented numerical simulations is to study the heat transport and to evaluate the efficiency by varying flow rates. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 80
    Publication Date: 2013-11-30
    Description: Partitioned coupling approaches are a well-established solution strategy for the numerical treatment of multi-physical problems. The nature of the decoupled algorithm requires a repetitive data exchange to achieve a proper balance between the different fields concerned. In the case of non-matching meshes, the data transfer becomes of particular importance when the values of interest are only available at the local integration points. In this case, an additional interpolation scheme has to be initialized in order to assure an energy-conserving data transfer. This contribution looks at a thermo-viscoplastic material that requires the interpolation of history-dependent data onto the thermal mesh. We propose a technique employing a least-square fit procedure and present a numerical example demonstrating the accurate data transfer. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 81
    Publication Date: 2013-11-30
    Description: Es wird ein Berechnungsmodell vorgestellt, mit dem eine numerischen Analyse der Strömungsvorgänge innerhalb von Schaufelwasserrädern möglich ist. Der Arbeitsschwerpunkt liegt dabei auf der strömungsmechanischen Optimierung von Hochleistungswasserrädern der Weiterentwickelten Wasserradtechnologie. In dem Berechnungsmodell werden die inkompressiblen Navier-Stokes-Gleichungen in den unabhängigen Variablen Geschwindigkeiten und Druck mit Hilfe der zeit-diskontinuierlichen Raum-Zeit-Finite-Elemente-Methode diskretisiert und die auftretende Gebietsveränderung infolge der sich drehenden Struktur mit der Shear-Slip Mesh Update Methode als diskontinuierlichem Netzbewegungsverfahren erfasst. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 82
    Publication Date: 2013-11-30
    Description: In this contribution, a macroscopic four-phase model, based on the Theory of Porous Media, is presented to simulate healing processes in a polymer matrix which depend on the amount (concentration) of catalysts. Therefore, the healing process is described by the phase transition from liquid like healing agents to solid like healed material. This phase transition is a function depending on the concentration. To show the applicability of the developed model, a numerical example will be presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 83
    Publication Date: 2013-11-30
    Description: In this communication, the Rodriguez method is proposed for modeling dynamics of the robotic system, where Lagrange's equations of second kind of rigid bodies system in covariant form are used. Discrete hybrid elements with so called piezo-modified Kelvin-Voight (PKV) and magnetorheological (MRD) type of viscoelastic models with fractional order derivatives are introduced in to the system of motion equations by means of generalized forces. The results obtained are illustrated by numerical examples. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 84
    Publication Date: 2013-11-30
    Description: In this paper we present two subjects of our actual research in the field. The first deals with the boundary conditions at the crack faces. The well known model by Hao and Shen gives opportunity to take the finite dielectric permeability of the crack into account, without having to solve the two- or three-dimensional coupled boundary value problem of solid material and crack medium. This approach, however, is based on the assumption of the electric field being perpendicular to the crack faces. We investigate this problem for arbitrary poling and field directions based on a combined analytical-numerical approach. The second focus of the paper is on the effective properties of piezoelectrics with cracks. Here, homogenization procedures are applied and extended towards coupled field problems including e.g. Maxwell stresses at internal boundaries and interfaces. Effective elastic, dielectric and piezoelectric constants exhibit interesting effects. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 85
    Publication Date: 2013-11-30
    Description: In this paper, a thermodynamically consistent small strain constitutive model is formulated that is directly based on the degree of cure, a key parameter in the curing (reaction) kinetics. The new formulation is also in line with the earlier proposed hypoelastic approach, cf. Hossain et al., 2010. The curing process of polymers is a complex phenomenon involving a series of chemical reactions which transform a viscoelastic fluid into a viscoelastic solid during which the temperature, the chemistry and the mechanics are coupled. Some representative numerical examples conclude the paper and show the capability of the newly proposed constitutive formulation to capture major phenomena observed during the curing processes of polymers. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 86
    Publication Date: 2013-11-30
    Description: In medicine a fundamental understanding for blood flow in human arteries is significantly important. In socalled hemodynamics engineers all over the world simulate blood flows in healthy and diseased vessels. Scientific findings in this area help to improve cardiovascular assisting devices and to plan surgical operations. The difficulty with such simulations is the interaction of the blood flow with the elastic vessel wall, which deforms due to changing flow conditions. We will present a two-dimensional model for blood flowing through an arterial vessel and investigate the balance of mass and the balance of linear momentum. We will adjust these balance equations appropriately and define time dependent boundary conditions. The necessary partial differential equations for the fluid-structure interaction will be solved by using the finite element method in FEniCS [1]. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 87
    Publication Date: 2013-11-30
    Description: Dielectric elastomers (DE's) are considered in recent times for the development of so called smart actuators. This relatively soft material is deformed under the influence of an external electric field. It is an ideal candidate for application in which complex surface deformations are desired. To increase the deformation range the insertion of material inclusions seems to be a good alternative. In the current work a mixed three field formulation in proposed to handle the quasi incompressibility of DE's for numerical simulations. A numerical analysis is performed in which the mixed formulation is compared with a standard displacement formulation. The results show the importance of the consideration of the nearly incompressible behaviour for the case of heterogeneous DE's. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 88
    Publication Date: 2013-11-30
    Description: The present work deals with the thermomechanical coupling in dissipative solids and the consistent temperature prediction. One of the first works dealing with this subject was written by Taylor & Quinney (TQ) where the fraction between dissipated energy eventually transformed to heat and plastic work is assumed as constant (typically between 0.8-1.0 for metals). Although this assumption often leads to reasonable temperature predictions, it is not always in agreement with experimental observations. Furthermore, the TQ model does not comply with the first and second law of thermodynamics in general. Unfortunately, a standard thermodynamically consistent framework is not convincing either, since it usually leads to a significant overprediction of the temperature increase during dissipative processes. Within the present work, a novel framework suitable for the modeling of thermomechanically coupled processes is discussed. It will be shown that this framework is thermodynamically consistent and leads to a temperature increase, as a result of plastic deformation, in good agreement with the underlying experiments. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 89
    Publication Date: 2013-11-30
    Description: A modeling and simulation approach for problems with solid-liquid-solid phase transitions and a free surface, feasible for material accumulation processes based on laser-based free form heading and welding processes for joining different metallic materials is presented. Both named processes are modeled within the framework of continuum mechanics by coupling the Stefan problem with the Navier-Stokes equations including a free capillary surface. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 90
    Publication Date: 2013-11-30
    Description: The major aim of this study is to show how to carry out the process of structural and parametrical synthesis that is understood as a design method of the system with active suppression of vibrations. Active components are implemented as electric components. The other objective is to analyze how the active subsystem interacts with the overall investigated structure. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 91
    Publication Date: 2013-11-30
    Description: In this paper the modelling by means of the different category graphs and analysis of vibrating subsystem of mechatronic systems by means of the exact and approximate methods have been presented. That approach was to nominate the relevance or irrelevance between the characteristics obtained by means of the exact method (only for the mechanical subsystem) and the approximate method. Such formulation concerns mostly the relevance of the natural frequencies-poles of the characteristics both mechanical subsystems and mechatronic systems. Approximate solutions requiring all the conditions for vibrating mechanical and/or mechatronic systems have been finding and it may be introduction to synthesis of these systems, modeled by different category graphs. Research limitation is following, that torsional vibrating continuous mechanical subsystem and mechatronic systems are linear type. Presentation the introduction to synthesis of considered class of mechatronic bar-systems with a constant changeable cross-section is practical implications of this work. Originality of such formulation is focused on the use of the different category graphs for modelling and synthesising by different methods represented by graphs of vibrating bars to the synthesis of considered discrete-continuous mechatronic systems. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 92
    Publication Date: 2013-11-30
    Description: For the description of the phase transformation effect TRIP (transformation induced plasticity), a thermo-micro-mechanical model is introduced. The scale transition is realized by a Hashin-Shtrikman type homogenization scheme. The macroscopical behavior is purely based on micro-mechanical, thermo-mechanical constitutive models. The model takes into account the thermal strains arising during cooling, and the Greenwood-Johnson effect. The Greenwood-Johnson effect describes the TRIP strain developing during the growth of a product phase in the parent phase. The TRIP strain is determined by a micromechanical model gained by an extended Leblond ansatz. For the diffusion driven phase transformation, the JMAK model is incorporated into the homogenization scheme. The diffusionless transformation is described by a rate law of Koistinen-Marburger type. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 93
    Publication Date: 2013-11-30
    Description: Since the microstructure of short fiber reinforced composites is inhomogeneous, the application of micromechanical models is useful, that take into account their characteristics like the fiber orientation and the aspect ratio of fibers. Two different methods are considered in this work: A two-step approach is utilized to get approximately the upper and lower bounds of the elastic properties. Furthermore, an approximation for the elastic properties is calculated by the self-consistence method. Both methods use discretely microstructural information including the length, the diameter and the orientation of each single fiber. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 94
    Publication Date: 2013-12-19
    Description: In this contribution we discuss the problem of a dislocation double pileup at impenetrable boundaries which serves as a benchmark test to examine the continuum dislocation dynamics (CDD). We enhance a formulation for a numerical implementation and the mean-field theory to account for the ‘long-range’ stress field due to inhomogeneous plastic deformations by a suitable correction term. This allows us to handle the motion of dislocation densities at impenetrable boundaries and study the influence of dislocation interactions on a scale much smaller than the scale of the proposed mean-field stress. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 95
    Publication Date: 2013-12-05
    Description: This contribution presents a method for the construction of three-dimensional Statistically Similar Representative Volume Elements (SSRVEs) for dual phase steels (DP steels). From such kind of advanced high strength steels, enhanced material properties are observed, which originate in the interaction of the individual constituents of the material on the microscale. Our aim is to directly incorporate the microstructure in the material modeling, which can be accomplished by applying i. e. the FE 2 method. A RVE representing the real material is used in the microscopic boundary value problem, which is solved at each macroscopic integration point. Since such RVEs usually exhibit a high complexity due to the underlying real microstructure, high computational costs are a drawback of the approach. We replace this RVE with a SSRVE, which has a lower complexity but which is still able to represent the mechanical behavior of the RVE and thus of the real microstructure. Virtual experiments show the performance of the method. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 96
    Publication Date: 2013-11-30
    Description: We present a de-coupled approach for computational modeling of liquid droplets moving on rough substrate surfaces. The computational model comprises solving the membrane deformation problem and the fluid flow problem in a segregated manner. The droplet shape is first computed by solving the Young-Laplace equation where contact constraints, due to the droplet-substrate contact, are applied through the penalty method [1]. The resulting configuration constitutes the domain for the fluid flow problem, where the bulk fluid behavior is modeled by the unsteady Stokes' flow model expressed in Arbitrary Lagrangian-Eulerian (ALE) framework. The entire analysis is performed in the framework of Finite Element Method (FEM). Application of the approach to the case of a droplet moving on a rough surface is presented as an example. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 97
    Publication Date: 2013-11-30
    Description: The numerical solution of coupled differential equation systems is usually done following a monolithic or a decoupled algorithm. In contrast to the holistic monolithic solvers, the decoupled solution strategies are based on breaking down the system into several subsystems. This results in different characteristics of these families of solvers, e. g., while the monolithic algorithms provide a relatively straight-forward solution framework, unlike their decoupled counterparts, they hinder software re-usability and customisation. This is a drawback for multi-field and multi-rate problems. The reason is that a multi-field problem comprises several subproblems corresponding to interacting subsystems. This suggests exploiting an individual solver for each subproblem. Moreover, for the efficient solution of a multi-rate problem, it makes sense to perform the temporal integration of each subproblem using a time-step size relative to its evolution rate. Nevertheless, decoupled solvers introduce additional errors to the solution and, thus, they must always be accompanied by a thorough stability analysis. Here, tailored solution schemes for the decoupled solution of multi-field and multi-rate problems are proposed. Moreover, the stability behaviour of the solutions obtained from these methods are studied. Numerical examples are solved and the reliability of the outcome of the stability analysis is investigated. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 98
    Publication Date: 2013-11-30
    Description: We consider a Stokes system and a Darcy system in a porous media, mutually coupled together by the the well-known Beaver-Joseph-Saffman interface conditions. Standard approaches use different finite elements in the two parts in order to account for the different stability properties of the two equation systems. In contrast to this, we use standard equal-order finite elements in both parts. Stability is obtained by adding local projection terms (LPS) to the Galerkin formulation. We formulate the scheme and give an a priori estimate. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 99
    Publication Date: 2013-11-30
    Description: Classical methods to calculate permeability of porous media have been proposed mainly for high density (e.g. granular) materials. These methods present shortcomings in high porosity, i.e. high permeability media (e.g. metallic foams). While for dense materials permeability seems to be a function of bulk properties and occupancy averaged over the volume, for highly porous materials these parameters fail to predict it. Several authors have attacked the problem by solving the Navier-Stokes equations for the pressure and velocity of a liquid flowing through a small domain (Ω s ) of aluminium foam and by comparing the numerical results with experimental values (prediction error approx. 9%). In this article, we present calculations for much larger domains (Ω L ) using the Finite Difference (FD) method, solving also for the pressure and velocity of a viscous liquid flowing through the Packed Spheres scenario. The ratio Vol (Ω L )/ Vol (Ω s ) is around 10 3 . The comparison of our results with the Packed Spheres example yields a prediction error of 5% for the intrinsic permeability. Additionally, numerical permeability calculations have been performed for Al foam samples. Our geometric modelling of the porous domain stems from 3D X-ray tomography, yielding voxel information, which is particularly appropriate for FD. Ongoing work concerns the reduction in computing times of the FD method, consideration of other materials and fluids, and comparison with experimental data. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 100
    Publication Date: 2013-11-30
    Description: Optimal control of mechanical systems is an active area of research. However, so far, most contributions are taking only one single objective into account, whereas for many practical problems, one is interested in optimizing several conflicting objectives at the same time. Applying singleobjective optimization to each of them leads to several trajectories each being optimal for one objective, but ignoring all others. In contrast to that, combining all objectives and using multiobjective optimization leads to a variety of trade off solutions taking all objectives into account simultaneously. We use the direct discretization method DMOCC (Discrete Mechanics and Optimal Control for Constrained systems) to approximate trajectories of the underlying optimal control problems, resulting in restricted optimization problems of high dimension. For the multiobjective part, we apply a reference point technique which successively utilizes an auxiliary distance function to gain the trade off solutions. The presented approach is illustrated by the multiobjective optimal control of a constrained multibody system. A four-body kinematic chain is controlled in a rest to rest maneuver, for which minimal control effort and minimal required maneuver time are the conflicting objectives. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
    Published by Wiley
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