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Issue ESAIM: M2AN
Volume 43, Number 3, May-June 2009
Page(s) 399 - 428
DOI 10.1051/m2an/2009009
Published online 08 April 2009

ESAIM: M2AN 43 (2009) 399-428
DOI: 10.1051/m2an/2009009

Numerical approaches to rate-independent processes and applications in inelasticity

Alexander Mielke1, 2 and Tomáš Roubíček3, 4

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 November 13, 2006. Revised January 31, 2008. Published online April 8, 2009.

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.


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


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