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Full Description
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.
Contents
The Many Roles of Viscosity in Solid Mechanics.- Multiscale Approach to a Basic Problem of Materials Mechanics (Propagation of Phase-Transition Fronts).- Section 1: Two and Multiphase Flows.- Analysing Particle Sedimentation in Fluids by Measure-Valued Stochastic Processes.- Phenomenological Model of Sedimentation-Consolidation Processes.- The Structure of Bidisperse Suspensions at Low Reynolds Numbers.- Lattice Boltzmann Simulations of Complex Multiphase Flows.- Interface Tracking in Multiphase Flows.- Section 2: Mechanics of Materials and Multiscaling.- Finite Element Computation of Macroscopic Quantities in Nonconvex Minimisation Problems and Applications in Materials Science.- Homogenization of an Initial-Boundary Value Problem Describing Evolving Microstructure.- Aspects of Homogenization Techniques and Multigrid Solving.- Estimates on the Mixture Function for Multiphase Problems in Elasticity.- A Two—Scale Micro—Macro—Approach to Anisotropic Finite Plasticity of Polycrystals.- Section 3: Solid—Fluid—Interaction.- Boundary Conditions at the Viscous Sliding Interface of Incompressible Porous Deformable Media.- Computational Experience from the Solution of Coupled Problems in Ship Dynamics.- On the Adaptive Computation of Shear Bands in Frictional Geomaterials.- Intrinsic Viscoelasticity of Porous Materials.- Numerical Simulation of Fluids Interacting with Moving Rigid Bodies.- Partitioned Analysis of Transient Nonlinear Fluid Structure Interaction Problems Including Free Surface Effects.- Section 4: Efficient Solvers and Adaptivity.- Domain Decomposition Methods in the Design of High Power Electronic Devices.- Matrix Compression for the Radiation Heat Transfer in Exhaust Pipes.- An Iterative Substructuring Method with Lagrange Multipliers for ElasticityProblems Using Approximate Neumann Subdomain Solvers.- A New a Posteriori Error Estimator in Adaptive Direct Boundary Element Methods. The Neumann Problem.- Efficient Elasto-Plastic Simulation.- Section 5: Contact and Fracture.- Sensitivity and Optimal Control in Contact Mechanics.- On the Treatment of Contact Problems in Elasto-Plasticity.- On Contact Problems for Linear and Nonlinear Elastic Plates: Existence of Solutions and Application of Augmented Lagrangian Method.- Longitudinal Wave Propagation in Conical Rods Subject to Impacts.- A Survey on Dynamic Contact Problems with Coulomb Friction.- Numerical Simulation of Noise Radiation from Rolling Tires.- Stress Singularities in Composites.
