Abstract
A system of invariants of symmetric three-dimensional tensors of second order is proposed. The system contains three classical invariants of a tensor and three new invariants which depend on the components of two or three tensors. The system proposed allows one to express the strain energy density of a linear elastic anisotropic body and virtual work done by internal stresses in terms of the invariants for any constitutive law of the material. Application of the invariants to the derivation of the tetrahedron finite element of anisotropic solids is discussed.
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