Circular shearing of compressible elastic cylinders

We consider the problem of circular shearing for compressible isotropic, homogeneous, hyperelastic right circular cylinders. First we consider the case of pure circular shearing where there is no radial displacement. We obtain necessary and sufficient conditions on the strain-energy function of the material for the existence of such a deformation. By considering several classes of strain-energy function we show that pure circular shearing is an exceptional deformation. However, we give three examples where pure circular shearing does exist and exact solutions are obtained.