Abstract
Necessary and sufficient conditions are given for the convexity of a scalar valued function of tensors that is proper isotropic, or invariant under rotations. These conditions are also appropriate for functions defined only for orientation preserving tensors. They are weaker than Ball's convexity conditions for fully isotropic functions (invariant under all orthogonal tensors) [B1]. The results are applied in obtaining polyconvexity conditions for the stored energy function.
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Rosakis, P. Characterization of Convex Isotropic Functions. Journal of Elasticity 49, 257–267 (1997). https://doi.org/10.1023/A:1007468902439
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DOI: https://doi.org/10.1023/A:1007468902439