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Numerical approaches to rate-independent processes and applications in inelasticity

Published online by Cambridge University Press:  08 April 2009

Alexander Mielke  and
Tomáš Roubíček
Alexander Mielke
Affiliation:
Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin, Germany. Institut für Mathematik, Humboldt Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin, Germany.
Tomáš Roubíček
Affiliation:
Mathematical Institute, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic. [email protected] Institute of Thermomechanics of the ASCR, Dolejškova 5, 182 00 Praha 8, Czech Republic.
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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 ofsubsequences of space-time discretizations even in case where the limitproblem does not have a unique solution and we need noadditional 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.

Keywords

Rate-independent evolutionenergetic solutionapproximationplasticitydamagedebondingmagnetostrictionmartensitic transformation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 3 , May 2009 , pp. 399 - 428
Copyright
© EDP Sciences, SMAI, 2009

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