Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution in terms of stochastic processes on a suitable probability space.

Keywords: quasistatic evolution, rate-independent processes, elastic materials, incremental problems, Young measures

@article{COCV_2009__15_2_245_0, author = {Fiaschi, Alice}, title = {A {Young} measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {245--278}, publisher = {EDP-Sciences}, volume = {15}, number = {2}, year = {2009}, doi = {10.1051/cocv:2008030}, mrnumber = {2513086}, zbl = {1161.74010}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2008030/} }

TY - JOUR AU - Fiaschi, Alice TI - A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 245 EP - 278 VL - 15 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2008030/ DO - 10.1051/cocv:2008030 LA - en ID - COCV_2009__15_2_245_0 ER -

%0 Journal Article %A Fiaschi, Alice %T A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 245-278 %V 15 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2008030/ %R 10.1051/cocv:2008030 %G en %F COCV_2009__15_2_245_0

Fiaschi, Alice. A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies. ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 2, pp. 245-278. doi : 10.1051/cocv:2008030. http://www.numdam.org/articles/10.1051/cocv:2008030/

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