paper

On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity

arXiv:0711.1479 · doi:10.1016/j.crme.2008.10.003

Abstract

If the constitutive law linking the second Piola-Kirchhoff stress tensor and the right Cauchy-Green strain tensor derives from a potential, then the Cauchy stress tensor and the logarithm of the left Cauchy-Green strain tensor are linked by a related potential. We give a new and concise proof which is based on an explicit formula expressing the derivative of the exponential of a tensor.

On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity · wovepaper