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

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

2007-11-09

arxiv.org/abs/0711.1479v1

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.crme.2008.10.003

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.

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