Bending History in Finite Element Inverse Analysis of Deep Drawing Processes

Abstract

This paper introduces a new approach to take account of bending history in finite element inverse analysis of a sheet metal forming process. A modified membrane element was adopted for finite element inverse analysis so that bending–unbending energy was additionally imposed on the total plastic energy. Bending–unbending regions were predicted from the geometry of the final shape and tools. The proposed method was applied to deep drawing processes of a cylindrical cup. The blank shape and the distribution of the thickness strain were compared with those obtained from the incremental finite element analysis to evaluate the effect of the bending history. The proposed method reduced the difference between the results of the inverse analysis and those of the incremental analysis. The analysis was also carried out changing 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 suggested method is useful to obtain more accurate results especially when bending effects are significant.