Finite element inverse analysis for the design of intermediate dies in multi-stage deep-drawing processes with large aspect ratio

An inverse finite element approach for multi-stage deep-drawing processes is introduced for robust capability to determine the optimum blank shape from the desired final shape and to obtain the thickness strain distribution in the final shape with a small amount of computing time and effort. A direct numerical analysis of multi-stage deep-drawing processes is extremely difficult to carry out because of its complexities and convergence problems as well as tremendous computing time. The analysis of elliptical or rectangular cup drawing with large aspect ratio is likewise very difficult with respect to the design process parameters including the intermediate die profiles. In order to overcome the difficulties, an inverse scheme is proposed in the present analysis and design. The multi-stage inverse analysis deals with the convergence among intermediate shapes and the corresponding sliding constraint surfaces. In this paper, finite element inverse analysis is applied to multi-stage deep-drawing processes in order to calculate the thickness strain distribution in each intermediate shape and to design the intermediate die shapes. The original design has been modified to enhance the discrepancy in the thickness strain distribution for each intermediate shape.