Abstract
For polyconvex stored energy mappings % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqef0uAJj3BZ9Mz0bYu% H52CGmvzYLMzaerbd9wDYLwzYbItLDharqqr1ngBPrgifHhDYfgasa% acOqpw0xe9v8qqaqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbba9q8Wq% Ffea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dme% aabiqaaiGacaGaamqadaabaeaafiaakeaadaqiaaqaaiabeo8aZbGa% ayPadaaaaa!4654!\[\widehat\sigma \], customary spatial and material symmetry requirements are shown to impose restrictions which are effective in the case of solids. Next, a generalized notion of material symmetry group is introduced, and it is shown that polyconvexity and infinite growth of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqef0uAJj3BZ9Mz0bYu% H52CGmvzYLMzaerbd9wDYLwzYbItLDharqqr1ngBPrgifHhDYfgasa% acOqpw0xe9v8qqaqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbba9q8Wq% Ffea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dme% aabiqaaiGacaGaamqadaabaeaafiaakeaadaqiaaqaaiabeo8aZbGa% ayPadaaaaa!4654!\[\widehat\sigma \](F) as det F → 0+ imply that all symmetry transformations must have unit determinant.
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Podio-Guidugli, P. Polyconvex energies and symmetry requirements. J Elasticity 26, 223–237 (1991). https://doi.org/10.1007/BF00041891
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DOI: https://doi.org/10.1007/BF00041891