Finite cylindrical deformations of a reinforced elastic tube

Abstract

We consider the deformation of an elastic and incompressible cylindrical tube of circular cross-section into a cylinder of a given shape under the action of end forces, uniform external pressure and normal forces applied on the inside surface. The outside surface of the undeformed tube is reinforced by a two parameter family of inextensible helical cords. The only restriction imposed on the cross-section of the deformed inside surface is that it has a continuous curvature. The equations are given for the general strain-energy function. Subsequently, it is assumed that the thickness of the tube is small compared to its overall diameter and the solutions to the equations are obtained, to the second order, for a neo-Hookean solid. Since the deformations considered are plane, the analysis is also valid for a Mooney-Rivlin material. Applications to specific boundary value problems are also given.