Numerical approaches to rate-independent processes and applications in inelasticity
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. firstname.lastname@example.org
4 Institute of Thermomechanics of the ASCR, Dolejškova 5, 182 00 Praha 8, Czech Republic.
Revised: 31 January 2008
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.
Mathematics Subject Classification: 35K85 / 49J40 / 49S05 / 65J15 / 65M12 / 65Z05 / 74C05 / 74F15 / 74H15 / 74N10 / 74R05 / 74S05
Key words: Rate-independent evolution / energetic solution / approximation / plasticity / damage / debonding / magnetostriction / martensitic transformation.
© EDP Sciences, SMAI, 2009