Numerical approaches to rate-independent processes and applications in inelasticity
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 3, pp. 399-428.

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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 : 10.1051/m2an/2009009
Classification : 35K85, 49J40, 49S05, 65J15, 65M12, 65Z05, 74C05, 74F15, 74H15, 74N10, 74R05, 74S05
Mots-clés : rate-independent evolution, energetic solution, approximation, plasticity, damage, debonding, magnetostriction, martensitic transformation 
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     title = {Numerical approaches to rate-independent processes and applications in inelasticity},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {399--428},
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Mielke, Alexander; Roubíček, Tomáš. Numerical approaches to rate-independent processes and applications in inelasticity. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 3, pp. 399-428. doi : 10.1051/m2an/2009009. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2009009/

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