Axisymmetric finite anti-plane shear of compressible nonlinearly elastic circular tubes

Abstract

The axial shear problem for a hollow circular cylinder, composed of homogeneous isotropic <italic>compressible</italic> nonlinearly elastic material, is described. The inner surface of the tube is bonded to a rigid cylinder while the outer surface is subjected to a uniformly distributed axial shear traction and the radial traction is zero. For an arbitrary compressible material, the cylinder will undergo both a radial and axial deformation. These axisymmetric fields are governed by a coupled pair of nonlinear ordinary differential equations, one of which is second-order and the other first-order. The class of materials for which <italic>axisymmetric anti-plane</italic> shear (i.e., a deformation with zero radial displacement) is possible is described. The corresponding axial displacement and stresses are determined explicitly. Specific material models are used to illustrate the results.