Pure azimuthal shear of compressible non-linearly elastic circular tubes

Open Access
Publisher Website
Google Scholar
Abstract
The azimuthal (or circular) shear problem for a hollow circular cylinder, composed of homogeneous isotropic compressible nonlinearly elastic material, is described. The inner surface of the tube is bonded to a rigid cylinder. The deformation may be achieved either by applying a uniformly distributed azimuthal shear traction on the outer surface together with zero radial traction (Problem 1) or by subjecting the outer surface to a prescribed angular displacement, with zero radial displacement (Problem 2). For an arbitrary compressible material, the cylinder will undergo both a radial and angular 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 pure azimuthal shear (i.e., a deformation with zero radial displacement) is possible is described. The corresponding angular displacement and stresses are determined explicitly. Specific material models are used to illustrate the results.

This publication has 19 references indexed in Scilit: