On Strain Energy Functions for Isotropic Elastic Materials

Abstract

This article deals with isotropic elasticmaterials which possess a strain energy function. For such materials the strain energy of a material point is given, of course, by a symmetric function σ̄ of the principal stretches v 1, v 2, v 3 at that point. It is known that a necessary condition to have an isotropic material compatible with the axioms for thermostatics proposed by Coleman and Noll is that the function σ̄ be jointly and strictly convex in its three variables v 1, v 2, v 3. Here we show that this condition is not sufficient for compatibility with the thermostatic axioms.