Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility

The purpose of this research is to investigate the simple torsion problem f or a solid circular cylinder composed of isotropic hyperelastic incompressi ble materials with limiting chain extensibility. Three popular models that account for hardening at large deformations are examined. These models invo lve a strain-energy density which depends only on the first invariant of th e Cauchy-Green tensor. In the limit as a polymeric chain extensibility tend s to infinity, all of these models reduce to the classical neo-Hookean form . The main mechanical quantities of interest in the torsion problem are obt ained in closed form. In this way, it is shown that the torsional response of all three materials is similar. While the predictions of the models agre e qualitatively with experimental data, the quantitative agreement is poor as is the case for the neo-Hookean material. In fact, by using a global uni versal relation, it is shown that the experimental data cannot be predicted quantitatively by any strain-energy density which depends solely on the fi rst invariant. It is shown that a modification of the strain energies to in clude a term linear in the second invariant can be used to remedy this defe ct. Whether the modified strain-energies, which reflect material hardening, are a feasible alternative to the classic Mooney-Rivlin model remains an o pen question which can be resolved only by large strain experiments.