Tension/torsion of electroactive solid cylinders

Abstract

In his pioneering work in nonlinear elasticity, Rivlin studied the tension–torsion of a solid isotropic homogeneous elastic cylinder and obtained expressions for the twisting moment as well as the normal force for all bodies belonging to that class in terms of the angle of twist and the stretch. The deformation considered by Rivlin was a universal controllable deformation in that it can be engendered by just the application of the appropriate surface tractions. In this short note we consider the tension–torsion of a solid electroelastic cylinder under the action of an electric field along the axis of the cylinder, and determine expressions for the twisting moment and normal force that depend on the angle of twist, stretch and the applied electric field. We obtain an expression for the torsional rigidity of the electroelastic solid cylinder that depends on the electric field, thereby implying its torsional rigidity can be “tuned” by varying the electrical field. While within the context of classical Cauchy elasticity one observes the compression of the isotropic solid cylinder, namely the POYNTING effect, we show that the cylinder can be made shorter or longer by controlling the electrical field.