Different implementations of inverse finite element method in sheet metal forming

During the recent years, application of the Inverse finite element method (IFEM) in prediction of the optimum blank from the desired final shape in stamping parts has been increased significantly. There are two basic formulations in inverse finite element method with this regard: (1) nonlinear formulation, and (2) linear formulation. Linear formulation can be obtained by developing an appropriate guess for unknown displacement vector. The main objective in the present work is to compare the basic formulations and capabilities of them. Advantages and disadvantages of these approaches such as type of solution, equations solving time and speed of convergence will be discussed. Both methodologies will be applied to deep drawing of a circular part and an oil pan to predict the blank shape. It will be shown that the CPU time used in the linear formulation is considerably lower than the nonlinear formulation. The comparison displays that the strain results obtained by both IFEM methods are somehow similar.