Numerical approaches to rate-independent processes and applications in inelasticity

¹ Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin, Germany.
² Institut für Mathematik, Humboldt Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin, Germany.
³ Mathematical Institute, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic. roubicek@karlin.mff.cuni.cz
⁴ Institute of Thermomechanics of the ASCR, Dolejškova 5, 182 00 Praha 8, Czech Republic.

Received: 13 November 2006
Revised: 31 January 2008

Abstract

A conceptual numerical strategy for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The novelty is that we obtain convergence of subsequences of space-time discretizations even in case where the limit problem does not have a unique solution and we need no additional assumptions on higher regularity of the limit solution. The variety of general perspectives thus obtained is illustrated on several specific examples: plasticity with isotropic hardening, damage, debonding, magnetostriction, and two models of martensitic transformation in shape-memory alloys.