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A covariant constitutive description of anisotropic nonlinear elasticity. (English) Zbl 0969.74010

Summary: We address the role of covariance in the constitutive description of anisotropic nonlinear elastic solids embedded in smooth manifolds. The covariant nature of material symmetry groups and associated structural tensors is discussed, and an equivalence is established between covariance of strain energy functions, inclusive of structural tensors and the respective anisotropic response. Also, we derive necessary conditions for covariance of anisotropic strain energy functions and alternative representations of the stress response.

MSC:

74B20 Nonlinear elasticity
74E10 Anisotropy in solid mechanics
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