A Note on the Torsion of an Incompressible Highly-Elastic Cylinder

In a previous paper (1), it has been shown that a state of simple torsion in a cylinder of incompressible highly elastic material, isotropic in its un-deformed state, may be produced by the application of surface tractions to the plane ends of the cylinder. In the deformation, each circular section of the cylinder normal to its axis is rotated, in its own plane, through an angle ψz, where z is the distance of the plane from one end of the cylinder. W is the stored-energy function for the material, given in terms of two strain invariants I₁ and I₂. The system of surface tractions which must be applied to each plane end of the cylinder in order to maintain the state of deformation is (i) a tangential surface traction Θ _v , azimuthal in the deformed state, and (ii) a normal surface traction Z _v , taken positive when in the direction of the outward drawn normal to the surface.