A simplified approach for incorporating thickness stress in the analysis of sheet metal forming using shell elements

A simplified scheme for considering the thickness stress of shell elements induced by contact is presented which improves the accuracy of sheet metal forming analysis. The yield function formulated on the basis of plane stress conditions is modified to incorporate the effect of transverse normal stress induced by contact forces acting on shell elements and return mapping routine is used to update in-plane stresses at each time step. The transverse normal stress distributions in the thickness direction are determined using the analytic solution of the cylindrical tube under the internal pressure. As numerical examples, uni-axial compression, bi-axial tension and bending tests are treated. The problem of cylindrical cup drawing is also calculated. Each result is compared with the results obtained by the analysis using ABAQUS continuum elements.