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.
Mots clés : rate-independent evolution, energetic solution, approximation, plasticity, damage, debonding, magnetostriction, martensitic transformation
@article{M2AN_2009__43_3_399_0,
author = {Mielke, Alexander and Roub{\'\i}\v{c}ek, Tom\'a\v{s}},
title = {Numerical approaches to rate-independent processes and applications in inelasticity},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {399--428},
publisher = {EDP-Sciences},
volume = {43},
number = {3},
year = {2009},
doi = {10.1051/m2an/2009009},
mrnumber = {2527399},
zbl = {1166.74010},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2009009/}
}
TY - JOUR AU - Mielke, Alexander AU - Roubíček, Tomáš TI - Numerical approaches to rate-independent processes and applications in inelasticity JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 399 EP - 428 VL - 43 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2009009/ DO - 10.1051/m2an/2009009 LA - en ID - M2AN_2009__43_3_399_0 ER -
%0 Journal Article %A Mielke, Alexander %A Roubíček, Tomáš %T Numerical approaches to rate-independent processes and applications in inelasticity %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 399-428 %V 43 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2009009/ %R 10.1051/m2an/2009009 %G en %F M2AN_2009__43_3_399_0
Mielke, Alexander; Roubíček, Tomáš. Numerical approaches to rate-independent processes and applications in inelasticity. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 3, pp. 399-428. doi : 10.1051/m2an/2009009. http://www.numdam.org/articles/10.1051/m2an/2009009/
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