Convex optimization and limit analysis: Application to Gurson and porous Drucker–Prager materials

First, we summarize our convex optimization method to solve the static approach of limit analysis. Then, we present the main features of a quadratic extension of a recently proposed mixed finite element method of the kinematic approach. Both methods are applied to obtain precise solutions to a forming problem with Gurson and Drucker–Prager materials. Finally, in order to analyze the criterion of “Porous Drucker–Prager” materials, the Gurson micro–macro model involving a Drucker–Prager matrix containing cylindrical cavities is investigated. Comparing previous results shows, among other things, a similarity in the compression case not always observed for the “Porous von Mises” material between cylindrical and spherical cases.