A covariant constitutive description of anisotropic non-linear elasticity

This article addresses the role of covariance in the constitutive descripti on of anisotropic non-linear elastic solids embedded in smooth manifolds. T he covariant nature of material symmetry groups and associated structural t ensors is discussed and an equivalence is Established between covariance of strain energy functions inclusive of structural tensors and the respective anisotropic response. Also, necessary conditions for covariance of anisotr opic strain energy functions and alternative representations of the stress response are derived.