Extension and torsion of rubber-like hollow and solid circular cylinders for incompressible isotropic hyperelastic materials with limiting chain extensibility

Abstract

In this paper we demonstrate the application of a newly proposed generalised neo-Hookean strain energy function within the family of limiting chain extensibility models to the problem of extension and torsion in incompressible isotropic rubber-like tubes and solid circular cylinders. We consider a general deformation involving extension and torsion in tubes, and subsequently specialise to the simple torsion of solid cylinders. Expressions for the twisting moment M, axial load N and the inflation pressure P (for tubes) are derived and presented for all the considered deformations. Using the proposed model, solutions are obtained for the critical axial stretch λcz beyond which the specimens exhibit the reversal of the Poynting-type effect upon twisting for both stretched tubes and solid cylinders. Furthermore, it will be demonstrated that the response function of the model is compatible with Penn and Kearsley's scaling law in torsion and can be directly derived from the ensuing experimental data. While the problem of torsion in elastic tubes and cylinders has been well-studied, this work provides a contribution to nuanced aspects of this problem including the prediction of the critical axial stretch λcz at which Poynting-type effects reverse in stretched specimens and the demonstration of compatibility with the scaling law of Penn and Kearsley.