A tensorial Hencky measure of strain and strain rate for finite deformations

Abstract

A proper tensorial logarithmic strain measure and its associated time rate of change is developed using an equivalence between the expressions for an isotropic tensor function and the Sylvester-Lagrange formalism. It is shown that the specific Cauchy stress T/ρ is derivable from a potential with respect to this strain measure. A modified stress TF is shown to be derivable from a potential with respect to the left polar decomposition of the deformation gradient. Advantages and disadvantages of this formulation are discussed.