# 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

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topMielke, 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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