CIRCULAR SHEARING OF COMPRESSIBLE ELASTIC CYLINDERS

We consider the problem of circular shearing for compressible isotropi c, homogeneous, hyperelastic right circular cylinders. First we consid er the case of pure circular shearing where there is no radial displac ement. We obtain necessary and sufficient conditions on the strain-ene rgy 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 solu tions are obtained. We also generate a new class of strain-energy func tions that exhibit pure circular shearing and again, exact solutions a re given. Finally some numerical examples for the general circular she aring problem are given.