ISBN: 3540675116
TITLE: Multifield Problems
AUTHOR: Sndig, A.-M.; Schiehlen, W.; Wendland, W.L. (Eds.)
TOC:

The Many Roles of Viscosity in Solid Mechanics
Stuart S. Antman 1
1. Introduction 1
2. A two-dimensional shearing problem 1
3. Self-sustained oscillations of a viscoelastic layer 4
4. Longitudinal motions 5
5. Longitudinal motions of incompressible rods 6
6. The motion of rods in space 8
7. Shocks and viscosity 9
References 10
Multiscale Approach to a Basic Problem of Materials Mechanics (Propagation of Phase-Transition Fronts)
Grard A. Maugin 11
1. Introduction 11
2. Microscopic condensed-matter-physics approach: solitonics 12
3. Macroscopic engineering approach: singular surface and thermodynamic criterion 13
4. Mesoscopic applied-mathematics approach: structured front 16
5. Theoretical-physics approach: quasi-particle and transient motion 16
6. Numerics: from finite-differences to continuous cellular automata 17
6.1 Finite-Difference Method 17
6.2 Finite-Element Method 18
6.3 Finite-Volume Method and cellular automaton 18
7. Conclusion 19
References 21
Section 1: Two and Multiphase Flows
Edited by H. Herrmann and S. Schwarzer 23
Analysing Particle Sedimentation in Fluids by Measure-Valued Stochastic Processes
Christian Hesse and Armin Dunz 25
1. Introduction 25
2. System analysis by measure-valued stochastic processes 27
3. Sedimentation in 1-d 30
References 33
Phenomenological Model of Sedimentation-Consolidation Processes
R. Brger 34
1. Introduction 34
2. Phenomenological sedimentation-consolidation model 34
3. Analysis of the initial-boundary value problem 37
4. Comparison with experimental data 38
5. Conclusions and directions of future research 40
References 40
The Structure of Bidisperse Suspensions at Low Reynolds Numbers
K. Hfler and S. Schwarzer 42
1. Introduction 42
2. Numerical method 42
3. Bidisperse suspensions 44
4. An advection-diffusion model for polydisperse suspensions 46
References 49
Lattice Boltzmann Simulations of Complex Multiphase Flows
M. Krafczyk, P. Lehmann, O. Filippova, D. Hnel and U. Lantermann 50
1. Lattice-Boltzmann simulation of gas-particle flow in complex geometry 50
1.1 Introduction 50
1.2 Method and results 51
2. Direct calculation of hysteresis by Lattice-Boltzmann simulations 54
2.1 Introduction 54
2.2 Hysteresis 54
2.3 Method and results 55
2.4 Discussion 56
2.5 Acknowledgements 57
References 57
Interface Tracking in Multiphase Flows
A.-K. Tornberg and B. Engquist 58
1. Introduction 58
2. The multiphase flow equations 59
2.1 Discretization 60
3. The segment projection method 62
4. Comparison of three methods for a buoyant bubble 63
References 65
Section 2: Mechanics of Materials and Multiscaling
Edited by C. Miehe 67
Finite Element Computation of Macroscopic Quantities in Nonconvex Minimisation Problems and Applications in Materials Science
Sren Bartels, Carsten Carstensen and Petr Plechc 69
1. Introduction 69
2. Scalar double-well problem and its numerical solution 71
3. Numerical analysis of linearised phase transitions in elastic solids 76
References 79
Homogenization of an Initial-Boundary Value Problem Describing Evolving Microstructure
Hans-Dieter Alber 80
1. Introduction 80
2. A mathematical model with sharp phase interfaces 80
2.1 Equations for the stress, displacement and internal variables 80
2.2 Evolution equation for the phase interface, dissipation inequality 82
3. Homogenization of the equations for materials
with evolving microstructure 85
References 87
Aspects of Homogenization Techniques and Multigrid Solving
C. G. Bayreuther, C. Miehe and J. Schrder 88
1. Introduction 88
2. The basic multigrid concept 88
3. A numerical homogenization procedure 90
4. Transfer operators for heterogeneous structures 91
4.1 Smoothing adapted transfer operators 91
4.2 Transfer operators associated with unit displacements 92
4.3 Algebraical motivated transfer operators 92
4.4 Homogenization based transfer operators 93
5. Comparative study of model problems 93
6. Conclusion 95
References 95
Estimates on the Mixture Function for Multiphase Problems in Elasticity
Alexander Mielke 96
1. Introduction 96
2. Definition of the mixture function 97
3. The H-measure associated with chi 99
4. A lower estimate 100
5. Upper bounds 101
6. A special case 102
References 103
A Two-Scale Micro-Macro-Approach to Anisotropic Finite Plasticity of Polycrystals
C. Miehe and J. Schotte 104
1. Introduction 104
2. A class of mirco-macro-transitions at large strains 105
3. A computational model of finite crystal plasticity 108
4. Texture evolution in homogeneous compression test 110
References 111
Section 3: Solid-Fluid-Interaction
Edited by W. Ehlers 113
Boundary Conditions at the Viscous Sliding Interface of Incompressible Porous Deformable Media
G.A. Ateshian and X. Wang 115
1. Introduction 115
2. Formulation 116
2.1 Kinematic conditions 117
2.2 Interface tractions 118
3. Limiting cases 120
3.1 Solid-solid interface 121
3.2 Fluid-fluid interface 121
3.3 Solid-fluid interface 121
3.4 Biphasic-fluid interface 121
3.5 Biphasic-solid interface 121
3.6 Inviscid fluid phase 122
4. Governing equations 122
5. Discussion 123
References 123
Computational Experience from the Solution of Coupled Problems in Ship Dynamics
Frank Ihlenburg 125
1. Introduction 125
2. Physical assumptions and governing equations 125
3. Numerical method and computational implementation 127
4. Computational results 127
4.1 Fluid-structure interaction 128
4.2 Structural model adaptation 130
4.3 Structural mesh refinement 132
5. Conclusions 132
References 134
On the Adaptive Computation of Shear Bands in Frictional Geomaterials
Wolfgang Ehlers and Peter Ellsiepen 135
1. Introduction 135
2. Governing equations 136
3. Spatial discretization and numerical tools 138
4. Numerical example 141
References 142
Intrinsic Viscoelasticity of Porous Materials
Wolfgang Ehlers and Bernd Markert 143
1. Introduction 143
2. Governing equations 144
3. Finite viscoelasticity law 145
4. Examples 147
5. Conclusions 149
References 150
Numerical Simulation of Fluids Interacting with Moving Rigid Bodies
S. Meynen and M. Schfer 151
1. Introduction 151
2. Governing equations and solution methods 152
2.1 Navier-Stokes equations for moving grids 152
2.2 Linear rigid body dynamics 153
3. Coupling algorithm 154
4. Numerical example 155
5. Conclusions 157
References 158
Partitioned Analysis of Transient Nonlinear Fluid Structure Interaction Problems Including Free Surface Effects
W.A. Wall, D.P. Mok, J. Schmidt and E. Ramm 159
1. Introduction 159
2. CFD - Computational Fluid Dynamics 159
2.1 Arbitrary Lagrangean Eulerian (ALE) formulation 160
2.2 Stabilized finite element method 160
2.3 Description of the free surface 161
3. CSD - Computational Structural Dynamics 161
4. CMD - Computational Mesh Dynamics 162
5. Partitioned staggered analysis approach 162
5.1 Algorithmic setup 163
5.2 A robust iterative substructuring scheme 164
6. Numerical examples 165
6.1 Floating vertical cylinder in viscous fluid 165
6.2 Cavity with oscillating top plate and exible bottom 165
References 166
Section 4: Efficient Solvers and Adaptivity
Edited by O. Steinbach and C. Wieners 167
Domain Decomposition Methods in the Design of High Power Electronic Devices
R. Hoppe, Y. Iliash, and G. Mazurkevitch 169
1. Introduction 169
2. High power electronic devices and systems 170
2.1 Electrothermomechanical couplings in IHV-Modules 170
2.2 Minimization of parasitic effects in Converter Modules 172
3. The mortar element methods 173
3.1 Mortar methods for Lagrangian finite elements 173
3.2 Mortar methods for curl-conforming edge elements 176
4. Numerical results 178
References 181
Matrix Compression for the Radiation Heat Transfer in Exhaust Pipes
M. Bebendorf and S. Rjasanow 183
1. Introduction 183
2. Mathematical model 184
3. Approximation of the full dense matrices 187
4. Adaptive cross approximation 188
4.1 Matrix partitioning 188
4.2 Low-rank approximation 189
5. Numerical examples 190
References 191
An Iterative Substructuring Method with Lagrange Multipliers for Elasticity Problems Using Approximate Neumann Subdomain Solvers
A. Klawonn 193
1. Introduction 193
2. The FETI method 194
3. The new domain decomposition method with approximate subdomain solves 196
4. Numerical results 198
References 200
A New a Posteriori Error Estimator in Adaptive Direct Boundary Element Methods. The Neumann Problem
H. Schulz and O. Steinbach 201
1. Introduction 201
2. An a posteriori error estimator 203
3. Implementation 205
4. Numerical example 207
References 208
Efficient Elasto-Plastic Simulation
C. Wieners 209
1. Introduction 209
2. A general framework for quasi-static plasticity 210
3. Return mapping algorithms for incremental plasticity 211
4. Standard materials 212
5. An example with nonlinear hardening 213
6. The computation of the return parameter 214
7. A numerical experiment 215
8. Conclusion 216
References 216
Section 5: Contact and Fracture
Edited by W. L. Wendland 217
Sensitivity and Optimal Control in Contact Mechanics
G. Szefer 219
1. Introduction 219
2. Setting of the optimal control and sensitivity problem 219
3. Adjoint system 225
4. Conclusions 228
References 228
On the Treatment ofContact Problems in Elasto-Plasticity
M. Bach, C. Eck and M. Schulz 229
1. Introduction 229
2. Problem setting 230
3. Boundary element method 234
4. Numerical example 236
References 236
On Contact Problems for Linear and Nonlinear Elastic Plates: Existence of Solutions and Application of Augmented Lagrangian Method
W. Bielski, A. Galka, and J.J. Telega 237
1. Geometrically linear plates 237
1.1 Thin plates 237
1.2 Reissner's plate model 239
2. Von Krmn plates 240
3. Augmented Lagrangians methods for a class of nonconvex problems 241
4. Example 243
References 245
Longitudinal Wave Propagation in Conical Rods Subject to Impacts
P. Eberhard, B. Hu and W. Schiehlen 246
1. Introduction 246
2. Symbolical computation for a conical rod 247
3. Experimental investigation of longitudinal waves 250
4. Conclusions 252
References 253
A Survey on Dynamic Contact Problems with Coulomb Friction
Ch. Eck and J. Jaruek 254
1. Introduction 254
2. The dynamic contact problem with Coulomb friction 254
3. Frictional contact problems with heat transfer 257
References 261
Numerical Simulation of Noise Radiation from Rolling Tires
L. Gaul, U. Nackenhorst and B. Nolte 262
1. Introduction 262
2. The simulation procedure 263
3. Numerical simulation of stationary rolling wheels 264
4. Numerical analysis of sound radiation 265
5. Example: A simple wheel 267
6. Conclusions 267
References 269
Stress Singularities in Composites
A.-M. Sndig 270
1. Introduction 270
2. Linear examples: Laplacian and Lam system 271
3. Linear elliptic boundary transmission problems in Sobolev spaces with detached asymptotics 274
4. Semilinear problems 275
5. Continuity and Frchet-differentiability of the semilinear operator 276
6. Asymptotic behaviour of the solution of the semilinear problem 276
References 277
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