Verification of the iterative procedure for solving the elastoplastic Kirsch problem on the Lame problem

Abstract

Abstract An iterative procedure for solving the elastoplastic Lame problem was proposed to further develop an iterative solution of the elastoplastic Kirsch problem. A ring under an external pressure is considered at which a certain plastic zone arises in the ring. The proposed iterative procedure for solving the elastoplastic Lame problem consists in an explicit analytical representation for stresses in the plastic region and the iterative technique for an elastic analytical solution. Furthermore, the plastic zone radius is beforehand unknown. The convergence of the iterative procedure for the elastoplastic Lame problem is shown in comparison with well-known analytical solution to this problem in elastoplastic formulation. A numerical-analytical iterative solution of the Lame problem in elastoplastic formulation is given for various external pressure and internal radius of the ring. Shows the convergence of numerical-analytical iterative solutions the problem in comparison with numerical solutions in elastoplastic formulation.