Torsion in nonlinearly elastic incompressible circular cylinders

We consider a variable torsion deformation for incompressible right-circular cylinders and investigate the possibility of equilibrium states other than simple torsion in isotropic hyperelasticity. Our problem formulation also provides generalized versions of Rivlin's universal relations in torsion. In this more general setting, it is shown that simple torsion persists as the only solution for large classes of strain energies. When one allows for more general boundary conditions, variable torsion solutions are possible for special forms of the stored energy function. We derive such a form and develop general results.