A Closed-form Solution to Finite Bending of a Compressible Elastic-perfectly Plastic Rectangular Block

Abstract

The self-consistent Eulerian rate-type elastoplastic model based on the logarithmic rate is used to study finite bending of a compressible elastic-perfectly plastic rectangular block. It is found that an explicit closed-form solution for this typical inhomogeneous finite deformation , mode may be available in a general case of compressible deformation with a stretch normal to the bending plane, where the maximum circumferential stretch at the outer surface serves as an Independent parameter. Expressions are given for the bending angle, the bending moment, the the outer and the inner radii, and the radii of the two moving elastic-plastic interfaces, etc. The exact stress distribution on any circumferential cross-section of the deformed block is accordingly determined.