A comparison of the Hart-Smith model with the Arruda-Boyce and Gent formulations for rubber elasticity

The present paper demonstrates that the Hart-Smith constitutive model and the more recent Arruda and Boyce eight chains and Gent constitutive models are closely related. The ability of these three models to predict both small and large strain responses of rubbers is highlighted and equations that relate their material parameters are established. INTRODUCTION Elastomers exhibit a very complex mechanical behavior, that includes large strain, timedependent response, hysteresis, and stress-softening (Mullins effect). In the last few years, there was a significant effort to propose realistic constitutive equations for these materials.1-10 These models focus on the whole behavior of elastomers or on only one of the previously mentioned phenomena. Nevertheless, all constitutive equations are based on the general theory of hyperelasticity.11 So, consider now the non-linear elastic response of rubber-like material. It is characterized by the existence of a strain energy potential W. Assuming that elastomers are both isotropic and incompressible, this strain energy function only depends on the two first invariants of the left Cauchy-Green stretch tensor B: