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.
@article{M2AN_2009__43_3_399_0,
author = {Mielke, Alexander and Roub\'\i \v cek, Tom\'a\v s},
title = {Numerical approaches to rate-independent processes and applications in inelasticity},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {43},
year = {2009},
pages = {399-428},
doi = {10.1051/m2an/2009009},
mrnumber = {2527399},
zbl = {1166.74010},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2009__43_3_399_0}
}
Mielke, Alexander; Roubíček, Tomáš. Numerical approaches to rate-independent processes and applications in inelasticity. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) pp. 399-428. doi : 10.1051/m2an/2009009. http://gdmltest.u-ga.fr/item/M2AN_2009__43_3_399_0/
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