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A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies. (English) Zbl 1161.74010
Summary: 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 that this result can be equivalently reformulated in probabilistic language and leads to the description of the quasistatic evolution in terms of stochastic processes in a suitable probability space.

74B20 Nonlinear elasticity
74G65 Energy minimization in equilibrium problems in solid mechanics
74H20 Existence of solutions of dynamical problems in solid mechanics
49Q20 Variational problems in a geometric measure-theoretic setting
49J55 Existence of optimal solutions to problems involving randomness
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