Irreducible expressions for isotropic functions of two tensors

Abstract

Polynomial expressions are given for scalar-valued, skew-symmetric second-order-tensor-valued and symmetric second-order-tensor-valued isotropic functions of two skew-symmetric second-order tensors, of one skew-symmetric and one symmetric second-order tensor and of two symmetric second-order tensors. It is shown that all terms of degree α, β in two tensors R, S (say) appearing in a given expression are linearly independent and that this is the case for all values of α and β.