This volume contains the contributions presented at the IUTAM Symposium on Variations of Domains and Free-Boundary Problems in Solid Mechanics, held in Paris, France, 22-25 April, 1997. In solid mechanics, free-boundary problems are relevant in a large variety of subjects such as optimization, optimal control, phase transition, metal casting, solidification and melting, stability analysis, inverse problems, propagating surface of discontinuity etc., and they raised interesting discussions in the past and recent literature. Although the physics behind these phenomena is immense, the mathematical analyses often present many common features. The three aspects - mechanical modelling, mathematical formulation and numerical resolution - are the outstanding points of this book. It gives a review of the state of the art in free-boundary problems for research engineers and researchers in applied mechanics and applied mathematics. The originality of this book is that it is solid mechanics oriented, whereas other books published in the same field are mathematics oriented.
Table of ContentsPreface. Steady State Solutions to a Multi-Dimensional Phase Change Problem in Ground Freezing; J.F. Rodrigues. Evolution of Phases in a Shape Memory Alloy by Local and Global Minimisations of a Non Convex Potentials; O. Maisonneuve, et al. Micromechanical Modelling of the Thermomechanical Behavior of Shape Memory Alloys by Local and Global Minimisations of a Non Convex Potentials; E. Patoor, M. Berveiller. Micromechanics Constitutive Modeling for Polycrystalline SMA; G.Q. Song, et al. Damping of a Vibrating SMA Rod Through Phase Trnasformation; E.R. Oberaigner, et al. The Equilibrium Motion of the Martensitic Interface in Thick-walled Infinite Austenitic Plate; B. Raniecki, Ch. Lexcellent. Error Control for Phase Change Problems; R.H. Nochetto, et al. Numerical Schemes for the Mean Curvature Flow of Graphs; G. Dziuk. Phase Diagrams - Heat of Mixing and Interfacial Energy; J. Ansorg, I. Müller. Propagation of a Front by Kink Motion; R. Abeyaratne, S. Vedantam. On Variational Aspects of the Theory of Liquid Crystals with Variable Degree of Orientation; Z. Naniewicz, P.D. Panagiotopoulos. Diffusion-Limited Dynamics in Growth Experiments; F. Agroul, et al. Molecular Dynamics Simulation of Melting / Solidification and Induced Stresses; T. Inoue, T. Uehara. Exploring the Commonality between Filling: Porous Media and Phase Change; V.R. Voller. About Nucleation and Growth; A. Visintin. Wavelet Methods for a Stefan Problem; J. Elezgaray, P. Petit. Delamination of Active Layers in Piezoelectric Laminates; P. Bisegna, F. Maceri. A Delamination Model: Mathematical Properties; N. Point, E. Sacco. Delamination Prediction by Continuum Damage Mechanics; O. Allix, et al. Dynamical Systems for Non-Isothermal Phase Separation; A.Damlamian, N. Kenmochi. Global Solution to the Penrose-Fife Phase Field Model with Special Heat Flux Laws; P. Colli, et al. Damage and Gradient of Damage in Transient Dynamics; B. Nedjar. Cracks in Fracture Mechanics: A Time Indexed Family of Energy Minimizers; G.A. Francfort, J.-J. Marigo. One-Dimensional Ductile-Brittle Transition, Yielding, and Structured Deformations; G. Del Piero. Approximation Results for a Class of Quasistatic Contact Problems Including Adhesion and Friction; M. Cocu, et al. A Continuous Model for Ziegler-Natta Polymerization; D. Andreucci, et al. A Steady Displacement-Based Formulation for the Analysis and Design of Large Deformation Continuous Elastoplastic Manufacturing Processes; D. Balagangadhar, D.A. Tortorelli. Strong Solutions to Equations of Visco-Thermo-Plasticity with a Temperature-Dependent Hysteretic Strain &endash; Stress Law; P. Krejcì, J. Sprekels. Thermomechanical Approach of Running Discontinuities; C. Stolz, R.M. Pradeilles-Duval. Global Solutions with Contact Discontinuities for Quasilinear Hyperbolic Systems of Conservation Laws; Li Ta-Tsien. Stability of a System Whose Boundary Evolutions are Governed by a Standard Constitutive Law; P. Berest. Stability of Moving Fronts under Griffith Criterion: A Computational Approach Using Integral Equations and Domain Derivatives; M. Bonnet. Instabilities Produced by Edges in Thin Shells; J.L. Lions, E. Sanchez-Palencia. On the Inversion of Subsurface Residual Stresses from Surface Stress Measurements; P. Ballard, A. Constantinescu. Structural Optimization by the Homogenization Method; G. Allaire, F. Jouve. Degenerate Sweeping Processes; M. Kunze, M.D.P. Monteiro Marques. About the Mathematical Modeling of Irreversibility Problems; P. Laborde. Sharp Energy Estim