PURE AZIMUTHAL SHEAR OF COMPRESSIBLE NONLINEARLY ELASTIC CIRCULAR TUBES

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 uniformiy 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.