Torsional instability of incompressible hyperelastic rubber-like solid circular cylinders with limiting chain extensibility

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 an instability problem in the torsion of incompressible isotropic rubber-like stretched solid circular cylinders. The instability of concern arises for sufficiently large twists where a kink or knot suddenly appears. An energy approach to investigation of this instability was given by Gent and Hua (2004) for a neo-Hookean elastic material, together with experimental observations on vulcanised rubber rods. We employ their framework in the present work on using the new limiting chain extensibility model. The model parameters are first obtained by fitting with experimental data for vulcanised rubber due to Gent and Hua. Then we use the instability criterion of Gent and Hua to calculate the critical twist at the onset of a knot formation with the new model. It is shown that the model provides more accurate predictions of the critical twisting angle at which the kink instability is initiated in vulcanised rubber compared with the neo-Hookean model used by Gent and Hua (2004). An alternative approach for slender thin rods proposed by Murphy (2015) is also implemented for the new model, and is shown to be a more tractable alternative method for limiting chain extensibility models.