Evaluating the response of a modified Gent-Thomas strain energy function having limiting chain extensibility condition in torsion and azimuthal shear

The purpose of this paper is to investigate the torsion and azimuthal shear of an incompressible hyperelastic cylinder having a modified Gent-Thomas strain energy with limiting chain extensibility condition. First, the torsional response of the modified Gent-Thomas model is obtained analytically and compared with those of Gent-Gent, Gent-Thomas, and Carroll strain energy models where the former model incorporates the limiting chain extensibility condition while the latter two are phenomenological models. The results show the modified Gent-Thomas model to be in better agreement with the experimental data of Rivlin and Saunders on torsion than the other three models. To further evaluate the response of the modified Gent-Thomas model, azimuthal shear deformation of an incompressible hyperelastic cylinder with the modified Gent-Thomas, Gent-Thomas, Gent-Gent, and Carroll strain energies is considered, where the angular displacement in azimuthal shear is determined analytically for the first three models and numerically for the fourth model. It is shown that the strain hardening effect, predicted either by the limiting chain extensibility condition for the modified Gent-Thomas and Gent-Gent models or phenomenologically by the Carroll model, is quite significant in the azimuthal shear response of the incompressible cylinder.

Symmetric Deformations of Viscoelastic-Plastic Cylinders

This paper, in the main, contains a general solution for a viscoelastic-plastic hollow circular cylinder under internal pressure and in the state of plane strain. The medium is assumed to be isotropic and homogeneous, and the constitutive equations used are a special case of those given in [1]. Solutions for both loading and unloading from a viscoelastic-plastic state are considered, and numerical results are obtained for the specific case of an incompressible cylinder under a step pressure. Also discussed briefly is the torsion of a viscoelastic-plastic cylinder, the solution of which is again illustrated by a numerical example.