Finite Element Inverse Analysis of the Deep Drawing Process Considering Bending History

Abstract

This paper introduces a new approach to take account of bending history in finite element inverse analysis during sheet metal forming process. A modified membrane element was adopted for finite element inverse analysis so that bending–unbending energy was additionally imposed in the total plastic energy, predicting bending–unbending regions using the geometry of the final shape and tools. An algorithm was applied to a cylindrical cup deep drawing process. The blank shape and the distribution of the thickness strain were compared with those obtained from the incremental finite element analysis in order to evaluate the effect of the bending history. The algorithm reduced the difference between the results of the inverse analysis from those of the incremental analysis due to bending history. The analysis was also carried out with the variation of the thickness of the initial blank to investigate the effect of bending deformation. The results showed that the difference was remarkably reduced as the thickness of the initial blank increased. This indicates that the finite element inverse analysis cooperated with the suggested scheme is useful to obtain more accurate results, especially when bending effects are significant.