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Frame-invariant polyconvex strain-energy functions for some anisotropic solids. (English) Zbl 1052.74012

This paper deals with a set of simple and realistic criteria guaranteeing the polyconvexity of the strain energy and hence the lower-semicontinuity of a large class of associated potential-energy functionals. The main goal is to extend previous criteria to certain anisotropic classes of materials which play an important role in current applications of finite elasticity and in bioelasticity, in particular. Specifically, the author develops criteria for polyconvexity of strain-energy functionals for materials having transversely isotropic or orthotropic symmetry relative to a specified reference state.

MSC:

74E10 Anisotropy in solid mechanics
74B20 Nonlinear elasticity
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