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arXiv · 0711.1479

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

Claude Vallee·Danielle Fortune·Camelia Lerintiu
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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.

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Claude Vallee, Danielle Fortune, Camelia Lerintiu. 2007-11-09. On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity. https://doi.org/10.1016/j.crme.2008.10.003

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