Finite elastic-plastic deformations of an ideal fibre-reinforced beam bent around a cylinder

Abstract

This paper considers the finite plane deformations of an initially straight beam composed of an elastic-plastic fibre-reinforced material. The reinforcing fibres are aligned along the beam. The effect of the fibres is to make the mechanical response of the composite material highly anisotropic, with the local fibre direction taking the role of the preferred direction. We assume the composite is incompressible and the fibres are continuously distributed throughout the material and deform with it. The composite is also assumed to be inextensible in the fibre direction. The beam is symmetrically bent around a smooth cylinder under the action of a uniform live load applied to its upper surface and is subsequently unloaded. Regions of plastic deformation are found during the loading phase and, if the applied forces are large enough, regions of reverse plastic yielding are found to occur during unloading. Non-trivial residual displacement and stress fields are determined when the beam is completely unloaded.

Professor Tryfan Rogers developed a fatal illness during the course of this work. He expressed a desire to be associated with the Naghdi Volume.