A new type of constitutive equation for nonlinear elastic bodies. Fitting with experimental data for rubber-like materials

Abstract

In this article, we develop a new implicit constitutive relation, which is based on a thermodynamic foundation that relates the Hencky strain to the Cauchy stress, by assuming a structure for the Gibbs potential based on the Cauchy stress. We study the tension/compression of a cylinder, biaxial stretching of a thin plate and simple shear within the context of our constitutive relation. We then compare the predictions of the constitutive relation that we develop and that of Ogden’s constitutive relation with the experiments of Treloar concerning tension/compression of a cylinder, and we show that the predictions of our constitutive relation provide a better description than Ogden’s model, with fewer material moduli.