Simulation of sheet metal forming processes by presenting a bending-dependent inverse isogeometric methodology

Recently, eliminating the gap between design and formability analysis of sheet metal parts has been studied to simulate sheet metal stamping processes. In this regard, a transfer-based inverse isogeometric formulation has been proposed. This method has various advantages such as solving the governing equations in two-dimensional networks without any concern about the convergence; however, it neglects the bending effect which is a major contributor in die/punch profile radii. The present work aims to consider the bending effects by introducing a bending-dependent inverse isogeometric formulation. The developed model deals with the minimization of potential energy, deformation theory of plasticity, classical plate theory, and considering a yield criterion in stress-resultant space. In addition to all advantages of the transfer-based inverse isogeometric formulation, one major benefit of this study is that the bending effects are included with a slight increase in the computation time. This methodology allows for accurately predicting the effects of changing die/punch profile radii and initial sheet thickness on the formability of the final part by presenting a new material updating process. To assess the credibility of this approach, an experimental setup and forward FEM software have been utilized to form a rectangular box. The results acquired by the developed method and those achieved by experiment and forward FEM reveal acceptable accuracy in the presented model. Also, strains and thicknesses predicted by the developed method, membrane inverse isogeometric model, and forward FEM for nine different values of punch radius to the sheet thickness ratio have been compared. Considering forward FEM as a reference method, the average of calculated error in the presented model for prediction of thickness at the middle of punch radius zone is around half of that in the membrane model. In solving the studied problems, the presented model requires only slightly more computation time (around 2%) than the membrane inverse isogeometric model and much less computation time than forward FEM. Therefore, the presented method is a valuable inverse forming solver especially when the bending effects are significant.