A stress integration algorithm for plane stress elastoplasticity and its applications to explicit finite element analysis of sheet metal forming processes

A stable stress integration algorithm of the elastoplastic constitutive equations for materials under a plane stress condition has been developed. In the algorithm, the trial stress obtained by elastic prediction is geometrically relaxed to the closest point on the yield surface in the principal stress plane. The direction of return-mapping is first obtained through the minimization problem using the Newton-Raphson method, and thereafter the plastic parameter is determined. As a model of yield criterion, Hill's quadratic normal anisotropic yield function has been adopted. The accuracy of the algorithm has been shown by iso-error maps for several materials. It has been revealed that errors are within 5% when the explicit time-integration method is adopted. In order to show the applicability of the algorithm, two kinds of sheet metal forming processes being able to represent various states of stress on the yield surface have been analyzed by FORMSYS-DE, the in-house explicit FEM code. The results of the simulations show good general coincidence with those of the experiments reported in the literature.