Two General Representation Theorems for Arbitrary‐Order‐Tensor‐Valued Isotropic and Anisotropic Tensor Functions of Vectors and Second Order Tensors

Abstract

AbstractIn this paper, it is shown that irreducible representations for r‐th‐order‐tensor‐valued isotropic or anisotropic tensor functions depending on an arbitrary number of vectors and second order tensors as variables may be formed by the union of irreducible representations for certain r‐th‐order‐tensor‐valued isotropic or anisotropic tensor functions merely depending on not more than three variables (for r ≧ 1) or four variables (for r = 0) and hence that the representation problem for the former may be reduced to that for the latter.