On third order tensor-valued isotropic functions

Abstract

Representation theorems for tensor-valued isotropic functions known until now are extended to enclose the third order ones; they consist in sets of tensorial functions, depending on an arbitrary number of vectors and second order tensors as variables, such that every other tensorial function of the same type can be expressed as a linear combination of the elements in the corresponding set, through scalar coefficients. Irreducibility of these sets is also proved in the sense that none of their proper subsets satisfies this property.