On helical shear of a compressible elastic circular cylindrical tube

In this paper we examine the combined azimuthal and axial shear of a compressible isotropic elastic circular cylindrical tube of finite extent, otherwise referred to as helical shear (which is an isochoric deformation). The equilibrium equations are formulated in terms of the principal stretches, and explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation are obtained and compared with those obtained previously for this problem. Several classes of strain-energy functions are derived and in some general cases complete solutions of the equilibrium equations are obtained. Existing results are recovered as special cases and some new results for the strain-energy functions derived are determined and discussed.