A unified theory of representations for scalar-, vector- and second order tensor-valued anisotropic functions of vectors and second order tensors

摘要

A substantial generalization of lokhi-Sedov-Boehler-Liu's isotropic extension method for representations of anisotropic tensor functions is suggested. It is shown that every scalar-, vector- and second order tensor-valued anisotropic tensor function with vector and second order tensor variables can be extended as an isotropic tensor function merely with augmented vector and second order tensor variables through some simple polynomial vector-valued and second order tensor-valued invariant ten- sor functions characterizing the anisotropy group.