AN EXACT FINITE DEFORMATION ELASTOPLASTIC SOLUTION FOR THE OUTSIDE-INFREE EVERSION PROBLEM OF A TUBE OF ELASTIC LINEAR-HARDENING MATERIAL

An exact solution is obtained in this paper for the elasto-plastic out side-in free eversion problem of a tube of elastic linear-hardening ma terial using a tensorial formulation. The solution is based on a finit e-strain version of Hencky's deformation theory, the von Mises yield c riterion, and the assumptions of volume incompressibility and axial le ngth constancy. All expressions for the stress, strain distributions a nd the eversion load are derived in an explicit form. In addition, wit h both the linear-elastic and strain-hardening-plastic responses of th e material being included and with the thickness effect of the tube be ing incorporated, this solution provides a rigorous and complete theor etical analysis of the elasto-plastic eversion problem, unlike existin g solutions. Two specific solutions are also presented as limiting cas es of the solution. Also provided are some numerical results and the r elated observations to show quantitatively applications of the solutio n.