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A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy. (English) Zbl 1167.74005

Summary: We study a quasistatic evolution problem for a nonconvex elastic energy functional. Due to lack of convexity, the natural energetic formulation can be obtained only in the framework of Young measures. Since the energy functional may present multiple wells, an evolution driven by global minimizers may exhibit unnatural jumps from one well to another one, which overcome large potential barriers. To avoid this phenomenon, we study a notion of solution based on a viscous regularization. Finally, we compare this solution with the one obtained with global minimization.

MSC:

74B20 Nonlinear elasticity
74H20 Existence of solutions of dynamical problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
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