An exact finite deformation elasto-plastic solution for the outside-in free eversion problem of a tube of elastic linear-hardening material

Abstract

An exact solution is obtained in this paper for the elasto-plastic outside-in free eversion problem of a tube of elastic linear-hardening material using a tensorial formulation. The solution is based on a finite-strain version of Hencky's deformation theory, the von Mises yield criterion, and the assumptions of volume incompressibility and axial length constancy. All expressions for the stress, strain distributions and the eversion load are derived in an explicit form. In addition, with both the linear-elastic and strain-hardening-plastic responses of the material being included and with the thickness effect of the tube being incorporated, this solution provides a rigorous and complete theoretical analysis of the elasto-plastic eversion problem, unlike existing solutions. Two specific solutions are also presented as limiting cases of the solution. Also provided are some numerical results and the related observations to show quantitatively applications of the solution.