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

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Vallee, Claude
Fortune, Danielle
Lerintiu, Camelia
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Abstract
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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.
Keywords
Mathematics - Analysis of PDEs, Mathematical Physics
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