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A Young measures approach to quasistatic evolutionfor a class ofmaterial models with nonconvexelastic energies

Published online by Cambridge University Press:  26 April 2008

Alice Fiaschi
Alice Fiaschi*
Affiliation:
SISSA, via Beirut 2-4, 34014 Trieste, Italy; fiaschi@sissa.it
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Abstract

Rate-independent evolution for material models with nonconvexelastic energies is studied without any spatial regularization ofthe inner variable; due to lack of convexity, the model is developedin the framework of Young measures. An existence result for thequasistatic evolution is obtained in terms of compatible systems ofYoung measures. We also show as this result can be equivalentlyreformulated with probabilistic language and leads to thedescription of the quasistatic evolution in terms of stochasticprocesses on a suitable probability space.

Keywords

Quasistatic evolutionrate-independent processeselastic materialsincremental problemsYoung measures

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Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 2 , April 2009 , pp. 245 - 278
Copyright
© EDP Sciences, SMAI, 2008

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