On general isotropic tensor functions of one tensor

This paper discusses general isotropic real symmetric tensor-valued functions of one real symmetric tensor. By exploiting the eigenprojection-based spectral representation of such functions, eigenprojectionbased closed formulae for the function derivatives are derived. The derived formulae provide an alternative to the eigenvector-based derivative expressions proposed by Chadwick and Ogden (Arch. Rat. Mech. Anal. 1971; 44:54–68) for the same class of functions and are an extension of the eigenprojection-based derivative expressions obtained by Carlson and Hoger (Quart. Appl. Math. 1986; 44(3):409–423) for a subset of the present class of functions. The material presented here is restricted to two- and three-dimensional spaces, which are of particular relevance to continuum mechanics. For completeness, algorithms for closed form computation of the isotropic tensor functions as well as their derivatives, based on the eigenprojection representation, are also presented. These should be of interest to computational mechanics researchers dealing with functions of the present type