Large Deformations of a Rotating Solid Cylinder for Non-Gaussian Isotropic, Incompressible Hyperelastic Materials

Abstract

The purpose of this research is to investigate the steady rotation of a solid cylinder for a class of strain-energy densities that are able to describe hardening phenomena in rubber. It is well known that use of the classic neo-Hookean strain energy gives rise to physically unrealistic response in this problem. In particular, solutions exist only for a sufficiently small angular velocity. As the velocity approaches this limiting value, the analysis predicts that the rotating cylinder collapses to a disk. It is shown here that this nonphysical behavior does not occur when generalized neo-Hookean models, which exhibit hardening at large deformations, are used.