Some Forms of the Strain Energy Function for Rubber

Abstract According to Rivlin's Phenomenological Theory of Rubber Elasticity, the elastic properties of a rubber may be described in terms of a strain energy function which is an infinite power series in the strain invariants I 1 , I 2 and I 3 . The simplest forms of Rivlin's strain energy function are the neo -Hookean, which is obtained by truncating the infinite series to just the first term in I 1 , and the Mooney-Rivlin, which retains the first terms in I 1 and I 2 . Recently, we proposed a strain energy function which is a cubic in I 1 . Conceptually, the proposed function is a material model with a shear modulus that varies with deformation. In this paper, we compare the large strain behavior of rubber as predicted by these forms of the strain energy function. The elastic behavior of swollen rubber is also discussed.