Numerical approaches to rate-independent processes and applications in inelasticity
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 3, p. 399-428

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.

DOI : https://doi.org/10.1051/m2an/2009009
Classification:  35K85,  49J40,  49S05,  65J15,  65M12,  65Z05,  74C05,  74F15,  74H15,  74N10,  74R05,  74S05
Keywords: 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 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},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {3},
     year = {2009},
     pages = {399-428},
     doi = {10.1051/m2an/2009009},
     zbl = {1166.74010},
     mrnumber = {2527399},
     language = {en},
     url = {http://www.numdam.org/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, Volume 43 (2009) no. 3, pp. 399-428. doi : 10.1051/m2an/2009009. http://www.numdam.org/item/M2AN_2009__43_3_399_0/

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