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Multifield Problems : State of the Art - Anna-Margarete Sandig

Multifield Problems

State of the Art

By: Anna-Margarete Sandig (Editor), W. O. Schiehlen (Editor), Wolfgang L. Wendland (Editor), Wolfram Ehlers (Editor), Hans J. Herrmann (Editor)

Hardcover Published: 15th June 2000
ISBN: 9783540675112
Number Of Pages: 278

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This book on the state of the art in "Multifield Problems" consists of selected articles based on a conference on this topic at the University of Stuttgart in 1999. The first two articles are contributions to the general modelling of multifield problems. S.S. Antman presents the important role of viscoelastic dissipation in the mathematical modelling of bifurcation analysis of nonlinear elasticity for large deformations. G.A. Maugin presents the basic theoretical foundations for the combination of three scales - the microscopic lattice of crystals, the mesoscopic thermomechanical model and the macroscopic con- tinuum mechanics model for describing the propagation of phase transition fronts in terms of the Landau-Ginzburg theory and the modelling of nonlinear waves. The other contributions are associated with five main areas of multifield modelling such as two and multiphase flows, the mechanics of materials in terms of multiscaling, the interaction of solids and fluids, efficient solution methods of the discrete equations including adaptivity, and the modelling of contact and fracture.

The Many Roles of Viscosity in Solid Mechanicsp. 1
Introductionp. 1
A two-dimensional shearing problemp. 1
Self-sustained oscillations of a viscoelastic layerp. 4
Longitudinal motionsp. 5
Longitudinal motions of incompressible rodsp. 6
The motion of rods in spacep. 8
Shocks and viscosityp. 9
Referencesp. 10
Multiscale Approach to a Basic Problem of Materials Mechanics (Propagation of Phase-Transition Fronts)p. 11
Introductionp. 11
Microscopic condensed-matter-physics approach: solitonicsp. 12
Macroscopic engineering approach: singular surface and thermody-namic criterionp. 13
Mesoscopic applied-mathematics approach: structured frontp. 16
Theoretical-physics approach: quasi-particle and transient motionp. 16
Numerics: from finite-differences to continuous cellular automatap. 17
Finite-Difference Methodp. 17
Finite-Element Methodp. 18
Finite-Volume Method and cellular automatonp. 18
Conclusionp. 19
Referencesp. 21
Two and Multiphase Flowsp. 23
Analysing Particle Sedimentation in Fluids byMeasure-Valued Stochastic Processesp. 25
Introductionp. 25
System analysis by measure-valued stochastic processesp. 27
Sedimentation in 1-dp. 30
Referencesp. 33
Phenomenological Model of Sedimentation-Consolidation Processesp. 34
Introductionp. 34
Phenomenological sedimentation-consolidation modelp. 34
Analysis of the initial-boundary value problemp. 37
Comparison with experimental datap. 38
Conclusions and directions of future researchp. 40
Referencesp. 40
The Structure of Bidisperse Suspensions at Low Reynolds Numbersp. 42
Introductionp. 42
Numerical methodp. 42
Bidisperse suspensionsp. 44
An advection-diffusion model for polydisperse suspensionsp. 46
Referencesp. 49
Lattice Boltzmann Simulations of Complex Multiphase Flowsp. 50
Lattice-Boltzmann simulation of gas-particle flow in complex geometryp. 50
Introductionp. 50
Method and resultsp. 51
Direct calculation of hysteresis by Lattice-Boltzmann simulationsp. 54
Introductionp. 54
Hysteresisp. 54
Method and resultsp. 55
Discussionp. 56
Acknowledgementsp. 57
Referencesp. 57
Interface Tracking in Multiphase Flowsp. 58
Introductionp. 58
The multiphase flow equationsp. 59
Discretizationp. 60
The segment projection methodp. 62
Comparison of three methods for a buoyant bubblep. 63
Referencesp. 65
Mechanics of Materials and Multiscalingp. 67
Finite Element Computation of Macroscopic Quantities in Nonconvex Minimisation Problems and Applications in Materials Sciencep. 69
Introductionp. 69
Scalar double-well problem and its numerical solutionp. 71
Numerical analysis of linearised phase transitions in elastic solidsp. 76
Referencesp. 79
Homogenization of an Initial-Boundary Value Problem Describing Evolving Microstructurep. 80
Introductionp. 80
A mathematical model with sharp phase interfacesp. 80
Equations for the stress, displacement and internal variablesp. 80
Evolution equation for the phase interface, dissipation inequalityp. 82
Homogenization of the equations for materials with evolving microstructurep. 85
Referencesp. 87
Aspects of Homogenization Techniques and Multigrid Solvingp. 88
Introductionp. 88
The basic multigrid conceptp. 88
A numerical homogenization procedurep. 90
Transfer operators for heterogeneous structuresp. 91
Smoothing adapted transfer operatorsp. 91
Transfer operators associated with unit displacementsp. 92
Algebraical motivated transfer operatorsp. 92
Homogenization based transfer operatorsp. 93
Comparative study of model problemsp. 93
Conclusionp. 95
Referencesp. 95
Estimates on the Mixture Function for Multiphase Problems in Elasticityp. 96
Introductionp. 96
Definition of the mixture functionp. 97
The <$>{cal H}<$>-measure associated with p. 99
A lower estimatep. 100
Upper boundsp. 101
A special casep. 102
Referencesp. 103
A Two-Scale Micro-Macro-Approach to Anisotropic Finite Plasticity of Polycrystalsp. 104
Introductionp. 104
A class of mirco-macro-transitions at large strainsp. 105
A computational model of finite crystal plasticityp. 108
Texture evolution in homogeneous compression testp. 110
Referencesp. 111
Solid-Fluid-Interactionp. 113
Boundary Conditions at the Viscous Sliding Interface of Incompressible Porous Deformable Mediap. 115
Introductionp. 115
Formulationp. 116
Kinematic conditionsp. 117
Interface tractionsp. 118
Limiting casesp. 120
Solid-solid interfacep. 121
Fluid-fluid interfacep. 121
Solid-fluid interfacep. 121
Biphasic-fluid interfacep. 121
Biphasic-solid interfacep. 121
Inviscid fluid phasep. 122
Governing equationsp. 122
Discussionp. 123
Referencesp. 123
Computational Experience from the Solution of Coupled Problems in Ship Dynamicsp. 125
Introductionp. 125
Physical assumptions and governing equationsp. 125
Numerical method and computational implementationp. 127
Computational resultsp. 127
Fluid-structure interactionp. 128
Structural model adaptationp. 130
Structural mesh refinementp. 132
Conclusionsp. 132
Referencesp. 134
On the Adaptive Computation of Shear Bands in Frictional Geomaterialsp. 135
Introductionp. 135
Governing equationsp. 136
Spatial discretization and numerical toolsp. 138
Numerical examplep. 141
Referencesp. 142
Intrinsic Viscoelasticity of Porous Materialsp. 143
Introductionp. 143
Governing equationsp. 144
Finite viscoelasticity lawp. 145
Examplesp. 147
Conclusionsp. 149
Referencesp. 150
Numerical Simulation of Fluids Interacting with Moving Rigid Bodiesp. 151
Introductionp. 151
Governing equations and solution methodsp. 152
Navier-Stokes equations for moving gridsp. 152
Linear rigid body dynamicsp. 153
Coupling algorithmp. 154
Numerical examplep. 155
Conclusionsp. 157
Referencesp. 158
Partitioned Analysis of Transient Nonlinear Fluid Structure Interaction Problems Including Free Surface Effectsp. 159
Introductionp. 159
CFD - Computational Fluid Dynamicsp. 159
Arbitrary Lagrangean Eulerian (ALE) formulationp. 160
Stabilized finite element methodp. 160
Description of the free surfacep. 161
CSD - Computational Structural Dynamicsp. 161
CMD - Computational Mesh Dynamicsp. 162
Partitioned staggered analysis approachp. 162
Algorithmic setupp. 163
A robust iterative substructuring schemep. 164
Numerical examplesp. 165
Floating vertical cylinder in viscous fluidp. 165
Cavity with oscillating top plate and flexible bottomp. 165
Referencesp. 166
Efficient Solvers and Adaptivityp. 167
Domain Decomposition Methods in the Design of High Power Electronic Devicesp. 169
Introductionp. 169
High power electronic devices and systemsp. 170
Eleetrothermomeehanieal couplings in IHV-Modulesp. 170
Minimization of parasitic effects in Converter Modulesp. 172
The mortar element methodsp. 173
Mortar methods for Lagrangian finite elementsp. 173
Mortar methods for curl-conforming edge elementsp. 176
Numerical resultsp. 178
Referencesp. 181
Matrix Compression for the Radiation Heat Transfer in Exhaust Pipesp. 183
Introductionp. 183
Mathematical modelp. 184
Approximation of the full dense matricesp. 187
Adaptive cross approximationp. 188
Matrix partitioningp. 188
Low-rank approximationp. 189
Numerical examplesp. 190
Referencesp. 191
An Iterative Substructuring Method with Lagrange Multipliers for Elasticity Problems Using Approximate Neumann Subdomain Solversp. 193
Introductionp. 193
The FETI methodp. 194
The new domain decomposition method with approximate subdomain solvesp. 196
Numerical resultsp. 198
Referencesp. 200
A New a Posteriori Error Estimator in Adaptive Direct Boundary Element Methods. The Neumann Problemp. 201
Introductionp. 201
An a posteriori error estimatorp. 203
Implementationp. 205
Numerical examplep. 207
Referencesp. 208
Efficient Elasto-Plastic Simulationp. 209
Introductionp. 209
A general framework for quasi-static plasticityp. 210
Return mapping algorithms for incremental plasticityp. 211
Standard materialsp. 212
An example with nonlinear hardeningp. 213
The computation of the return parameterp. 214
A numerical experimentp. 215
Conclusionp. 216
Referencesp. 216
Contact and Fracturep. 217
Sensitivity and Optimal Control in Contact Mechanicsp. 219
Introductionp. 219
Setting of the optimal control and sensitivity problemp. 219
Adjoint systemp. 225
Conclusionsp. 228
Referencesp. 228
On the Treatment of Contact Problems in Elasto-Plasticityp. 229
Introductionp. 229
Problem settingp. 230
Boundary element methodp. 234
Numerical examplep. 236
Referencesp. 236
On Contact Problems for Linear and Nonlinear Elastic Plates: Existence of Solutions and Application of Augmented Lagrangian Methodp. 237
Geometrically linear platesp. 237
Thin platesp. 237
Reissner's plate modelp. 239
Von Kármán platesp. 240
Augmented Lagrangians methods for a class of nonconvex problemsp. 241
Examplep. 243
Referencesp. 245
Longitudinal Wave Propagation in Conical Rods Subject to Impactsp. 246
Introductionp. 246
Symbolical computation for a conical rodp. 247
Experimental investigation of longitudinal wavesp. 250
Conclusionsp. 252
Referencesp. 253
A Survey on Dynamic Contact Problems with Coulomb Frictionp. 254
Introductionp. 254
The dynamic contact problem with Coulomb frictionp. 254
Frictional contact problems with heat transferp. 257
Referencesp. 261
Numerical Simulation of Noise Radiation from Rolling Tiresp. 262
Introductionp. 262
The simulation procedurep. 263
Numerical simulation of stationary rolling wheelsp. 264
Numerical analysis of sound radiationp. 265
Example: A simple wheelp. 267
Conclusionsp. 267
Referencesp. 269
Stress Singularities in Compositesp. 270
Introductionp. 270
Linear examples: Laplacian and Lamé systemp. 271
Linear elliptic boundary transmission problems in Sobolev spaces with detached asymptoticsp. 274
Semilinear problemsp. 275
Continuity and Fréchet-differentiability of the semilinear operatorp. 276
Asymptotic behaviour of the solution of the semilinear problemp. 276
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540675112
ISBN-10: 3540675116
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 278
Published: 15th June 2000
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.91
Weight (kg): 0.61

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