Pure azimuthal shear of isotropic, incompressible hyperelastic materials with limiting chain extensibility

Abstract

The purpose of this research is to investigate the pure azimuthal shear problem for a circular cylindrical tube composed of isotropic hyperelastic incompressible materials with limiting chain extensibility. Three popular models that account for hardening at large deformations are examined. These involve a strain-energy density which depends only on the first invariant of the Cauchy–Green tensor. In the limit as a polymeric chain extensibility tends to infinity, all of these models reduce to the classical neo-Hookean form. The stress fields and axial displacements are characterized for each of these models. Explicit closed-form analytic expressions are obtained for two of the strain-energy densities considered. The results are compared with one another and with the predictions of the neo-Hookean model.