Numerical approaches to rate-independent processes and applications in inelasticity

Alexander Mielke; Tomáš Roubíček

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 3, page 399-428
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Mielke, Alexander, and Roubíček, Tomáš. "Numerical approaches to rate-independent processes and applications in inelasticity." ESAIM: Mathematical Modelling and Numerical Analysis 43.3 (2009): 399-428. <http://eudml.org/doc/250647>.

@article{Mielke2009,
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 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. },
author = {Mielke, Alexander, Roubíček, Tomáš},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Rate-independent evolution; energetic solution; approximation; plasticity; damage; debonding; magnetostriction; martensitic transformation.; magnetostriction; martensitic transformation; convergence},
language = {eng},
month = {4},
number = {3},
pages = {399-428},
publisher = {EDP Sciences},
title = {Numerical approaches to rate-independent processes and applications in inelasticity},
url = {http://eudml.org/doc/250647},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Mielke, Alexander
AU - Roubíček, Tomáš
TI - Numerical approaches to rate-independent processes and applications in inelasticity
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/4//
PB - EDP Sciences
VL - 43
IS - 3
SP - 399
EP - 428
AB - 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.
LA - eng
KW - Rate-independent evolution; energetic solution; approximation; plasticity; damage; debonding; magnetostriction; martensitic transformation.; magnetostriction; martensitic transformation; convergence
UR - http://eudml.org/doc/250647
ER -

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