An analytic benchmark solution to the problem of a generalized plane strain hollow cylinder made of micromorphic plastic porous metal and subjected to axisymmetric loading conditions

Abstract

We provide a full analytical solution for the problem of a generalized plane strain circular hollow cylinder subjected to axisymmetric loading conditions. The matrix of the cylinder obeys a micromorphic plasticity theory as proposed by Gologanu, Leblond, Perrin and Devaux. The solution gives explicit expressions for the displacement, the strain and its gradient, as well as the ordinary and generalized stress fields. The newly derived solution satisfies the equilibrium equations and is shown to be an extension of the solution of the same model problem using (von Mises) classical plasticity theory.