A new approach to solve key issues in multi-step inverse finite-element method in sheet metal stamping

Multi-step inverse finite-element method (FEM) has been introduced to improve the accuracy of simulation in the sheet metal stamping. Moreover, it has also been used to try to obtain the strain distribution and shape of the blank in the intermediate steps. But there are two key problems which are essential for the realization of multi-step inverse FEM: the first one is the determination of initial solutions on the intermediate three-dimensional (3-D) configurations and the other is how to control the movement of nodes only on sliding constraint surfaces during Newton–Raphson iterations. In the study, the two questions above have been solved with our proposed methods: the former is obtained by mapping the arc-length of the final part onto intermediate sliding constraint surfaces with modified arc-length search method, and the latter is conducted by introducing an approach which is similar to that of contact search. The present inverse multi-step FEM has been realized and applied to a two-step deep drawing product. The obtained numerical results have been used to compare with that of incremental FEM to evaluate the effectiveness of the procedures proposed. Comparisons between multi-step inverse FEM and one-step inverse FEM have also been conducted to verify the effect of multi-step.