Multifield Problems

The Many Roles of Viscosity in Solid Mechanics

(11)

Stuart S. Antman

Introduction

(1)

A two-dimensional shearing problem

(3)

Self-sustained oscillations of a viscoelastic layer

(1)

Longitudinal motions

(1)

Longitudinal motions of incompressible rods

(2)

The motion of rods in space

(1)

Shocks and viscosity

(2)

References

(1)

Multiscale Approach to a Basic Problem of Materials Mechanics (Propagation of Phase-Transition Fronts)

(12)

Gerard A. Maugin

Introduction

(1)

Microscopic condensed-matter-physics approach: solitonics

(1)

Macroscopic engineering approach: singular surface and thermodynamic criterion

(3)

Mesoscopic applied-mathematics approach: structured front

(1)

Theoretical-physics approach: quasi-particle and transient motion

(1)

Numerics: from finite-differences to continuous cellular automata

(2)

Finite-Difference Method

(1)

Finite-Element Method

(1)

Finite-Volume Method and cellular automation

(1)

Conclusion

(4)

References

(2)

Section 1: Two and Multiphase Flows

(44)

H. Herrmann

S. Schwarzer

Analysing Particle Sedimentation in Fluids by Measure-Valued Stochastic Processes

(9)

Christian Hesse

Armin Dunz

Introduction

(2)

System analysis by measure-valued stochastic processes

(3)

Sedimentation in 1-d

(4)

References

(1)

Phenomenological Model of Sedimentation-Consolidation Processes

(8)

R. Burger

Introduction

(1)

Phenomenological sedimentation-consolidation model

(3)

Analysis of the initial-boundary value problem

(1)

Comparison with experimental data

(2)

Conclusions and directions of future research

(2)

References

(2)

The Structure of Bidisperse Suspensions at Low Reynolds Numbers

(8)

K. Hofler

S. Schwarzer

Introduction

(1)

Numerical method

(2)

Bidisperse suspensions

(2)

An advection-diffusion model for polydisperse suspensions

(4)

References

(1)

Lattice Boltzmann Simulations of Complex Multiphase Flows

(8)

M. Krafczyk

P. Lehmann

O. Filippova

D. Hanel

U. Lantermann

Lattice-Boltzmann simulation of gas-particle flow in complex geometry

(4)

Introduction

(1)

Method and results

(3)

Direct calculation of hysteresis by Lattice-Boltzmann simulations

(4)

Introduction

(1)

Hysteresis

(1)

Method and results

(1)

Discussion

(1)

Acknowledgements

(1)

References

(1)

Interface Tracking in Multiphase Flows

(9)

A.-K. Tornberg

B. Engquist

Introduction

(1)

The multiphase flow equations

(3)

Discretization

(2)

The segment projection method

(1)

Comparison of three methods for a buoyant bubble

(4)

References

(2)

Section 2: Mechanics of Materials and Multiscaling

(46)

C. Miehe

Finite Element Computation of Macroscopic Quantities in Nonconvex Minimisation Problems and Applications in Materials Science

(11)

Soren Bartels

Carsten Carstensen

Petr Plechac

Introduction

(2)

Scalar double-well problem and its numerical solution

(5)

Numerical analysis of linearised phase transitions in elastic solids

(4)

References

(1)

Homogenization of an Initial-Boundary Value Problem Describing Evolving Microstructure

(8)

Hans-Dieter Alber

Introduction

(1)

A mathematical model with sharp phase interfaces

(5)

Equations for the stress, displacement and internal variables

(2)

Evolution equation for the phase interface, dissipation inequality

(3)

Homogenization of the equations for materials with evolving microstructure

(3)

References

(1)

Aspects of Homogenization Techniques and Multigrid Solving

(8)

C. G. Bayreuther

C. Miehe

J. Schroder

Introduction

(1)

The basic multigrid concept

(2)

A numerical homogenization procedure

(1)

Transfer operators for heterogeneous structures

(2)

Smoothing adapted transfer operators

(1)

Transfer operators associated with unit displacements

(1)

Algebraical motivated transfer operators

(1)

Homogenization based transfer operators

(1)

Comparative study of model problems

(2)

Conclusion

(1)

References

(1)

Estimates on the Mixture Function for Multiphase Problems in Elasticity

(8)

Alexander Mielke

Introduction

(1)

Definition of the mixture function

(2)

The H-measure associated with X

(1)

A lower estimate

100

(1)

Upper bounds

101

(1)

A special case

102

(2)

References

103

(1)

A Two--Scale Micro--Macro--Approach to Anisotropic Finite Plasticity of Polycrystals

104

(9)

C. Miehe

J. Schotte

Introduction

104

(1)

A class of micro-macro-transitions at large strains

105

(3)

A computational model of finite crystal plasticity

108

(2)

Texture evolution in homogeneous compression test

110

(3)

References

111

(2)

Section 3: Solid--Fluid--Interaction

113

(54)

W. Ehlers

Boundary Conditions at the Viscous Sliding Interface of Incompressible Porous Deformable Media

115

(10)

G. A. Ateshian

X. Wang

Introduction

115

(1)

Formulation

116

(4)

Kinematic conditions

117

(1)

Interface tractions

118

(2)

Limiting cases

120

(2)

Solid-solid interface

121

(1)

Fluid-fluid interface

121

(1)

Solid-fluid interface

121

(1)

Biphasic-fluid interface

121

(1)

Biphasic-solid interface

121

(1)

Inviscid fluid phase

122

(1)

Governing equations

122

(1)

Discussion

123

(2)

References

123

(2)

Computational Experience from the Solution of Coupled Problems in Ship Dynamics

125

(10)

Frank Ihlenburg

Introduction

125

(1)

Physical assumptions and governing equations

125

(2)

Numerical method and computational implementation

127

(1)

Computational results

127

(5)

Fluid-structure interaction

128

(2)

Structural model adaptation

130

(2)

Structural mesh refinement

132

(1)

Conclusions

132

(3)

References

134

(1)

On the Adaptive Computation of Shear Bands in Frictional Geomaterials

135

(8)

Wolfgang Ehlers

Peter Ellsiepen

Introduction

135

(1)

Governing equations

136

(2)

Spatial discretization and numerical tools

138

(3)

Numerical example

141

(2)

References

142

(1)

Intrinsic Viscoelasticity of Porous Materials

143

(8)

Wolfgang Ehlers

Bernd Markert

Introduction

143

(1)

Governing equations

144

(1)

Finite viscoelasticity law

145

(2)

Examples

147

(2)

Conclusions

149

(2)

References

150

(1)

Numerical Simulation of Fluids Interacting with Moving Rigid Bodies

151

(8)

S. Meynen

M. Schafer

Introduction

151

(1)

Governing equations and solution methods

152

(2)

Navier-Stokes equations for moving grids

152

(1)

Linear rigid body dynamics

153

(1)

Coupling algorithm

154

(1)

Numerical example

155

(2)

Conclusions

157

(2)

References

158

(1)

Partitioned Analysis of Transient Nonlinear Fluid Structure Interaction Problems Including Free Surface Effects

159

(8)

W. A. Wall

D. P. Mok

J. Schmidt

E. Ramm

Introduction

159

(1)

CFD - Computational Fluid Dynamics

159

(2)

Arbitrary Lagrangean Eulerian (ALE) formulation

160

(1)

Stabilized finite element method

160

(1)

Description of the free surface

161

(1)

CSD - Computational Structural Dynamics

161

(1)

CMD - Computational Mesh Dynamics

162

(1)

Partitioned staggered analysis approach

162

(3)

Algorithmic setup

163

(1)

A robust iterative substructuring scheme

164

(1)

Numerical examples

165

(2)

Floating vertical cylinder in viscous fluid

165

(1)

Cavity with oscillating top plate and flexible bottom

165

(1)

References

166

(1)

Section 4: Efficient Solvers and Adaptivity

167

(50)

O. Steinbach

C. Wieners

Domain Decomposition Methods in the Design of High Power Electronic Devices

169

(14)

R. Hoppe

Y. Iliash

G. Mazurkevitch

Introduction

169

(1)

High power electronic devices and systems

170

(3)

Electrothermomechanical couplings in IHV-Modules

170

(2)

Minimization of parasitic effects in Converter Modules

172

(1)

The mortar element methods

173

(5)

Mortar methods for Lagrangian finite elements

173

(3)

Mortar methods for curl-conforming edge elements

176

(2)

Numerical results

178

(5)

References

181

(2)

Matrix Compression for the Radiation Heat Transfer in Exhaust Pipes

183

(10)

M. Bebendort

S. Rjasanow

Introduction

183

(1)

Mathematical model

184

(3)

Approximation of the full dense matrices

187

(1)

Adaptive cross approximation

188

(2)

Matrix partitioning

188

(1)

Low-rank approximation

189

(1)

Numerical examples

190

(3)

References

191

(2)

An Iterative Substructuring Method with Lagrange Multipliers for Elasticity Problems Using Approximate Neumann Subdomain Solvers

193

(8)

A. Klawonn

Introduction

193

(1)

The FETI method

194

(2)

The new domain decomposition method with approximate subdomain solves

196

(2)

Numerical results

198

(3)

References

200

(1)

A New a Posteriori Error Estimator in Adaptive Direct Boundary Element Methods. The Neumann Problem

201

(8)

H. Schulz

O. Steinbach

Introduction

201

(2)

An a posteriori error estimator

203

(2)

Implementation

205

(2)

Numerical example

207

(2)

References

208

(1)

Efficient Elasto-Plastic Simulation

209

(8)

C. Wieners

Introduction

209

(1)

A general framework for quasi-static plasticity

210

(1)

Return mapping algorithms for incremental plasticity

211

(1)

Standard materials

212

(1)

An example with nonlinear hardening

213

(1)

The computation of the return parameter

214

(1)

A numerical experiement

215

(1)

Conclusion

216

(1)

References

216

(1)

Section 5: Contact and Fracture

217

(2)

W. L. Wendland

Sensitivity and Optimal Control in Contact Mechanics

219

(1)

G. Szefer

Introduction

219

(1)

Setting of the optimal control and sensitivity problem

219

(6)

Adjoint system

225

(3)

Conclusions

228

(1)

References

228

(1)

On the Treatment of Contact Problems in Elasto-Plasticity

229

(1)

M. Bach

C. Eck

M. Schulz

Introduction

229

(1)

Problem setting

230

(3)

Boundary element method

234

(2)

Numerical example

236

(1)

References

236

(1)

On Contact Problems for Linear and Nonlinear Elastic Plates: Existence of Solutions and Application of Augmented Lagrangian Method

237

(1)

W. Bielski

A. Galka

J.J. Telega

Geometrically linear plates

237

(1)

Thin plates

237

(2)

Reissner's plate model

239

(1)

Von Karman plates

240

(1)

Augmented Lagrangians methods for a class of nonconvex problems

241

(2)

Example

243

(2)

References

245

(1)

Longitudinal Wave Propagation in Conical Rods Subject to Impacts

246

(1)

P. Eberhard

B. Hu

W. Schiehlen

Introduction

246

(1)

Symbolical computation for a conical rod

247

(3)

Experimental investigation of longitudinal waves

250

(2)

Conclusions

252

(1)

References

253

(1)

A Survey on Dynamic Contact Problems with Coulomb Friction

254

(1)

Ch. Eck

J. Jarusek

Introduction

254

(1)

The dynamic contact problem with Coulomb friction

254

(3)

Frictional contact problems with heat transfer

257

(4)

References

261

(1)

Numerical Simulation of Noise Radiation from Rolling Tires

262

(1)

L. Gaul

U. Nackenhorst

B. Nolte

Introduction

262

(1)

The simulation procedure

263

(1)

Numerical simulation of stationary rolling wheels

264

(1)

Numerical analysis of sound radiation

265

(2)

Example: A simple wheel

267

(1)

Conclusions

267

(2)

References

269

(1)

Stress Singularities in Composites

270

(1)

A.-M. Sandig

Introduction

270

(1)

Linear examples: Laplacian and Lame system

271

(3)

Linear elliptic boundary transmission problems in Sobolev spaces with detached asymptotics

274

(1)

Semilinear problems

275

(1)

Continuity and Frechet---differentiability of the semilinear operator

276

(1)

Asymptotic behaviour of the solution of the semilinear problem

276

(1)

References

277

Rent More, Save More! Use code: ECRENTAL

Rent More, Save More! Use code: ECRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

9783540675112

3540675116

Summary

Table of Contents

Supplemental Materials

Rewards Program

Rent More, Save More! Use code: ECRENTAL

Rent More, Save More! Use code: ECRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Multifield Problems

9783540675112

3540675116

Summary

Table of Contents

Supplemental Materials

Rewards Program

Digital License