Finite deformation elasto-plastic solution for the pure bending problem of a wide plate of elastic linear-hardening material

Abstract

An exact elasto-plastic analytical solution for a finitely deformed plane strain wide plate of elastic linear-hardening material subjected to pure bending is derived in this paper using a tensorial formulation. This solution is based on a finite-strain version of Hencky's deformation theory, the von Mises yield criterion and the incompressibility assumption. The Hencky (logarithmic) strain tensor is adopted to measure the finite deformations, with the undeformed flat plate as the reference configuration. The constitutive relations are derived in tensor form using the Hencky strain and the Cauchy stress. With both the linear-elastic and strain-hardening-plastic material responses included, the present solution can represent the whole bending process of the plate from its initial flat state to its final curved state with arbitrarily large deformation. It is shown that this solution exhibits general characteristics, from which three specific solutions of practical value can be obtained. Being expressed in both tensor and component forms, the present exact solution for the stress and strain fields furnishes a new and systematic analytical pattern for the elasto-plastic analysis and strength design of a strain-hardening wide plate subjected to large-deformation pure bending.