Inverse Finite Element Analysis of Sheet Metal Forming

In order to investigate the formability of sheet metals to the desired shapes and design the appropriate forming tools, accurate simulations of the forming process are required to avoid the time-consuming procedure of trial and error at the manufacturing stage and deliver flawless parts.

There are several influential parameters in the formability of sheet metals, such as the die geometry, blank initial shape, thickness, blank holder force, and contact condition between the tool and workpiece. The traditional approach to simulate the sheet metal forming process is the nonlinear forward incremental finite element, based on the flow theory of plasticity and exact modeling of deformation history, boundary and contact conditions, and material properties.

This strategy is precise, but computationally expensive too. Furthermore, prior knowledge of initial blank shape and process parameters is required, which is not the case in many industrial applications. Thus, over the past few decades, several new numerical tools have been developed to rapidly predict the strain distribution of the designed workpiece and asses its formability at preliminary design stages.

These techniques use the deformation theory to find the initial blank contour from the given final configuration, and then estimate strain distribution in the formed workpiece. Since all these techniques proceed from final to initial states, they are called one-step inverse simulations. This is what this project is about and below are some examples. Given the final desired shape we want to know the proper initial blank that could be used to form it into the final geometry without rupturing it (All through one-step inverse finite element method). Once the initial blank is known, the thickness distribution in the final geometry can also be computed.