The mechanics and mathematics of the effect of pressure on the shear modulus of elastomers

In this paper, we discuss the need for models that express the stretch (or strain) as a function of stress, or implicit constitutive models that relate the stretch (or strain) and stress, for describing the elastic response of some elastomers. We would like to provide an explanation for some experimental data for elastomeric materials that imply that the material moduli depend on pressure. Included in the class of models that are proposed are those which can explain limiting chain extensibility that is exhibited by some rubber-like solids. The models that are proposed stem from a completely different starting point from that for classical elastic bodies, so that these models cannot be obtained within the context of classical theory.