Torsion of an Isotropic Elastic Circular Cylinder

Abstract

It is shown that a static pure torsion can be imposed on a circular cylinder comprised of any homogeneous isotropic elastic material subject to suitable surface tractions alone if the material is incompressible, but such a pure torsion cannot generally be imposed if the material is compressible. Hence the static torsion is a universal deformation for an incompressible isotropic elastic material, but not for a compressible isotropic elastic material. The analysis of such a pure torsion is due to Rivlin (1947; 1948a; 1949a). A broader family of universal deformations of Ericksen & Rivlin (1954) is also discussed, where this larger family includes not only torsions but also extensions and inflations of a circular cylinder. The calculation of these and other universal exact solutions for finite elastic deformation represents a remarkable achievement in the mathematical theory of elasticity. The development here follows that of Truesdell & Noll (1965).