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Elastoplasticity of gradient-polyconvex materials. (English) Zbl 1477.35262

Summary: We propose a model for rate-independent evolution in elastoplastic materials under external loading, which allows large strains. In the setting of strain-gradient plasticity with multiplicative decomposition of the deformation gradient, we prove the existence of the so-called energetic solution. The stored energy density function is assumed to depend on gradients of minors of the deformation gradient which makes our results applicable to shape-memory materials, for instance.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
49J40 Variational inequalities
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
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