FInite torsion of slightly compressible rubberlike circular cylinders∗

A regular perturbation procedure and the Rayleigh-Ritz method are used to study the finite torsion of cylinders made of slightly compressible neo-Hookean materials. Two cases are considered: 1. the length of the cylinder is not permitted to change during torsion and 2. the net axial force on the cylinder vanishes. The perturbation procedure fails for certain constitutive relations whereas, in principle, the Rayleigh-Ritz method has general applicability. When it works, the success of the perturbation procedure depends on prior knowledge of the problem for an incompressible material (the zeroth order nonlinear problem). The solution of problem 2. is considerably more complicated than the solution of problem 1. since the complete approximation of order n for problem 2. requires extensive work on the approximation of order (n + 1).