Lu, Jia; Papadopoulos, Panayiotis A covariant constitutive description of anisotropic nonlinear elasticity. (English) Zbl 0969.74010 Z. Angew. Math. Phys. 51, No. 2, 204-217 (2000). 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. Cited in 16 Documents MSC: 74B20 Nonlinear elasticity 74E10 Anisotropy in solid mechanics Keywords:anisotropic nonlinear elastic solids; smooth manifolds; material symmetry groups; structural tensors; covariance of strain energy functions; stress response PDFBibTeX XMLCite \textit{J. Lu} and \textit{P. Papadopoulos}, Z. Angew. Math. Phys. 51, No. 2, 204--217 (2000; Zbl 0969.74010) Full Text: DOI