Elastic behaviour of rubber cylinders under combined torsion and tension loading

Abstract

Rivlin derived an elastic solution for the problem of a rubber cylinder subjected to combinations of tension and torsion. The theory correctly predicts the experimentally observed behaviour where the length of the cylinder increases as a twist is applied and conversely there is a reduction in the moment resulting from the application of an additional tensile loading. This problem is of interest for two reasons. First, the reduction in axial force with twist is second order by virtue of the change in the axial force being a symmetric function of the square of the twist angle. Therefore, the problem makes a demanding test of the applicability of the finite element method at solving this large strain elasticity problem. Second, the Rivlin elasticity solution could in principle be applied to any form of stored energy function. As a result, it is a useful test of the validity of different stored energy functions. Also, this test geometry has been examined previously by the authors to investigate any anisotropic changes in the viscoelastic behaviour in rubber with prestrain and it is important to validate the elastic solutions for this work.