Extensibility of rubber under different types of deformation

Abstract

The finite lengths of molecular strands in a crosslinked rubber network impose a limit on the extensibility because some of the strands become fully stretched. This feature must be taken into account in formulating a strain energy function W to describe the elastic response of rubber, especially for high strains. The question is: Are the maximum strains the same for different types of deformation, or different? Maximum strains are compared here for various types of homogeneous deformation: simple extension; simple shear and pure shear (constrained tension); and equibiaxial extension. The rubber is assumed to consist of a network of Gaussian strands that are randomly arranged in the unstrained state and deform affinely until representative strands become fully stretched, at a limiting value J1m of the first strain invariant, J1. Dickie and Smith (1971) showed that the extensibility in equibiaxial stretching is only about 70% of that in simple extension, in accord with a limiting value of J1. For other simple types of deformation the extensibilities are expected to be nearly equal. Possible deficiencies in the model and in the experiments are then considered. It is concluded that the general result is likely to be valid, and that a model for rubber elasticity at large strains should include a limiting value of the first strain invariant, J1, rather than the second, J2.