Continuum-Based Design Sensitivity Analysis and Optimization of Springback in Stamping Process

The springback is a significant manufacturing defect in the stamping process. A serious impediment to the use of lighter-weight, higher-strength materials in manufacturing is the relative lack of understanding about how these materials respond to the complex forming process. The springback problem can be reduced by using appropriate designs of die, punch, and blank holder shape together with friction and blank holding force. That is, an optimum stamping process can be determined using a gradient-based optimization to minimize the springback. However, for an effective optimization of the stamping process, development of an efficient analytical design sensitivity analysis method is crucial. In this paper, a continuum-based shape and configuration design sensitivity analysis (DSA) method for the stamping process has been developed. The material derivative concept is used to develop the continuum-based design sensitivity. The design sensitivity equation is solved without iteration at each converged load step in the finite deformation elastoplastic nonlinear analysis with frictional contact, which makes the design sensitivity calculation very efficient. The accuracy and efficiency of the proposed method is illustrated by minimizing springback in an S-rail part, which is often used as an industrial benchmark to verify the numerical procedures employed for stamping processes.