On Modelling Simple Shear for Isotropic Incompressible Rubber-Like Materials

In this paper we demonstrate the application of a recently proposed molecular based generalised neo-Hookean strain energy function within the family of limiting chain extensibility models to the simple shear of incompressible isotropic rubber-like hyperelastic materials. The two-parameter model of concern is capable of capturing both linear and highly nonlinear shear stress responses. It provides favourable simultaneous fits to experimental data for various components of the simple shear stress field, such as the shear stress and normal tractions/stresses, with a single set of parameter values. In addition, when used in a phenomenological context, the model also captures shear-softening behaviour and predicts an interesting instability. These modelling results are demonstrated in conjunction with a wide range of extant experimental data involving the simple shearing of biological tissue specimens and polymer and rubber samples. It will also be shown that in all these applications, the proposed model remains stable (convex) over the defined domain of deformation. These results underline the merits of the considered model for addressing some of the outstanding challenges in the constitutive modelling of the complex nonlinear behaviour of rubber-like materials.