POD Surrogate Models Using Adaptive Sampling Space Parameters for Springback Optimization in Sheet Metal Forming
The use of high strength steels for the stamping process in automotive body parts requires master spring back effects. Several parameters of the stamping process have an influence on springback effects. It is possible to optimize these parameters, but only way to achieve this optimization procedure is to use numerical simulation of the stamping process. Nevertheless, the optimization process requires an expensive evaluation of a high fidelity model over the whole design space. To reduce the overall computational cost, a surrogate model for the optimization process replaces the high fidelity model. Extensive design of numerical experiments on the overall design space of the high fidelity model is needed to build this surrogate model. To improve the efficiency of the overall optimization process, this paper presents Proper Orthogonal Decomposition (POD) surrogate models using adaptive sampling design space. Here the POD surrogate model aims to represent the final displacement field from the initial high-fidelity simulation and use the reduced basis and the radial basis functions (RBF) interpolation of the POD coefficient to describe and predict the final shape. During the optimization process, the new samples of the high-fidelity model are added using the minimization of the predicted objective function criterion. The proposed methodology is illustrated with the ``U-bend'' from the Numisheet2011 benchmark. Two parameters, the blank holder force and die radius are chosen to optimize the spring back effect.