Exact results for the problem of a hollow sphere subjected to hydrostatic tension and made of micromorphic plastic porous material

Abstract

We report an exact, analytical solution to the problem of a hollow sphere subjected to hydrostatic tension and made of ideal-plastic porous material, obeying a micromorphic model developed by Gologanu, Leblond, Perrin and Devaux (GLPD). The motivation is to find analytical solutions for simple problems that might be of interest to assess the robustness of the numerical implementation of the micromorphic model into finite element codes. We provide the details of the analytical calculations of the deformation, stress and moment distributions. We demonstrate the validity of our analytical results by comparing them to the solution of the classical problem of a hollow sphere whose matrix obeys the von Mises model, subjected to hydrostatic tension.