Geodesic
A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 2, pp. 245-278

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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.

DOI : 10.1051/cocv:2008030
Classification : 74B20, 28A33, 74G65, 49J45
Keywords: quasistatic evolution, rate-independent processes, elastic materials, incremental problems, Young measures 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv:2008030/}
}
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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, Tome 15 (2009) no. 2, pp. 245-278. doi: 10.1051/cocv:2008030

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