Pure torsion of compressible non-linearly elastic circular cylinders

Abstract

The large deformation torsion problem of an elastic circular cylinder, composed of homogeneous isotropic <italic>compressible</italic> nonlinearly elastic material and subjected to twisting moments at its ends, is described. The problem is formulated as a two-point boundary-value problem for a second-order nonlinear ordinary differential equation in the radial deformation field. The class of materials for which <italic>pure torsion</italic> (i.e., a deformation with zero radial displacement) is possible is described. Specific material models are used to illustrate the results.