A universal relation in torsion for a mixture of solid and fluid

In his study of combined finite extension and torsion of a nonlinear, incompressible, isotropic elastic circular cylinder, Rivlin [1] established a relation for the torsional stiffness which depends only on the axial force, the axial extension ratio and the radius of the undeformed cylinder, in the case of small twist. The relationship did not depend on the structure of the stored energy function and is hence a universal relation. In this paper, we extend Rivlin's result to the case of combined extension and torsion of a cylindrical mixture of a nonlinear elastic solid and fluid.