Developments of multi-step simulations in sheet metal forming processes

At the early design stage of sheet metal forming processes, the well-known inverse approach provides an efficient formability analysis for the pre-designed final part. However, the evaluation of stress state is poor due to its lack of consideration in deformation histories. In this paper, the finite element multi-step method is developed to improve the stress estimations by introducing several intermediate configurations, which are efficiently solved and constructed by using the pseudo minimum area approach and the initial solutions respectively. Therefore, the new nonlinear kinematics are formulated to provide the forward finite logarithmic strain increments, and the classical implicit local integration is performed to update the stress for the anisotropic elastoplastic material. Numerical simulations are carried out to validate the proposed method.