On symmetric tensor-valued isotropic functions of a symmetric tensor and a skewsymmetric tensor and related transversely isotropic functions

Abstract

A new generating set consisting of seven polynomial tensor generators is presented for symmetric second order tensor-valued isotropic functions of a symmetric second order tensor and a skewsymmetric second order tensor. It is smaller than the existing corresponding generating set consisting of eight tensor generators and shown to be minimal in all possible generating sets consisting of homogeneous polynomial tensor generators. This result indicates that the well-known results for isotropic functions may be sharpened. In addition, from the presented result, a minimal generating set consisting of six tensor generators is derived for the symmetric second order tensor-valued transversely isotropic functions of a symmetric second order tensor relative to the transverse isotropy group C_∞h consisting of all rotations about a fixed aixs.