Thermoelastic Behavior of Rubber-Like Materials at Large Deformations

The statistical theory of rubber-like elasticity requires the energy contribution (fe/f) to be independent of the applied strain. We have in recent publications demonstrated that this stipulation is satisfied within the framework of the statistical theory. However, since this theory is only valid up to moderate strains (∼30%), the question then arises as to how fe/f behaves at large deformations. In this paper we have examined this problem in the context of phenomenological theories of finite elasticity. It is shown that only for neo-Hookean strain energy function, which is equivalent to the statistical-theory free-energy function, is the value of fe/f a constant. For other strain energy functions, such as the Mooney-Rivlin and Valanis-Landel functions, fe/f must decrease with increasing strain. The implication is that in the elasticity of most real rubbers the intermolecular energies play a more important role than previously realized.