Comparison of two algorithms for the computation of fourth-order isotropic tensor functions

Abstract

This paper compares two possible representations of a certain class of fourth-order isotropic tensor functions. It focusses on the derivatives of symmetric second-order isotropic tensor functions by a symmetric second-order tensor argument. This tensor argument is assumed to be given in spectral form. The first representation explicitly needs the eigenvectors of the argument tensor and is well-known in the literature. The second representation proposed here is based on the knowledge of second-order eigenvalue bases and avoids the computation of eigenvectors. The evaluation of a typical model problem shows that the second representation needs less computer time than the first one. The representations discussed here are of high importance for numerical solvers of nonlinear initial-boundary-value problems in large-strain elasticity and elastoplasticity.