Some new solutions for the axial shear of a circular cylindrical tube of compressible elastic material

In this paper the axial shear deformation of a thick-walled right circular cylindrical tube of compressible isotropic elastic material is considered. Under the assumption that the deformation is isochoric the resulting two governing ordinary differential equations of equilibrium are combined to yield a necessary condition on the strain-energy function for the material to admit pure axial sheer (or anti-plane shear). For any strain-energy function satisfying this condition further conditions are required to guarantee the existence of solutions. Such conditions are discussed and used to obtain explicit solutions for several forms of strain-energy function. Existing results are recovered as a special case and new solutions are obtained for some specific strain-energy functions. It is then shown how the results may be used to generate solutions for the axial shear problem in incompressible materials. (C) 1999 Elsevier Science Ltd. All rights reserved.