Application of the Dunford‐Taylor Integral to Isotropic Tensor Functions

Abstract

In the present contribution closed‐form representations for isotropic tensor functions and their derivative are formulated using the Dunford‐Taylor integral. These representations are given in terms of eigenvalues of the tensor argument and are valid for all second‐order tensors defined as a linear mapping over the n‐dimensional real vector space. The solution obtained is especially useful for non‐symmetric tensor functions where representations based on the spectral decomposition in diagonal form cannot generally be applied.