Parametric modeling of an electromagnetic compression device with the proper generalized decomposition

Optimization of forming processes seeks an optimal choice of many process parameters. In Electromagnetic Material Forming (EMF), parameters associated to the geometry of the forming device or related to the generation of the pulsed currents have to be set, and are of primary importance to achieve the proper geometry of the formed part. Usual optimization procedures proceed by defining a trial choice of the set of parameters and then evaluate the optimality of a given cost function computed from a direct analysis. This iterative process requires many assessments of the cost function and may lead to a prohibitive computation cost since the direct analysis may involve a structural analysis. Others approaches have been proposed to circumvent this problem; based on a separated representation of the solution, the Proper Generalized Decomposition allows for a parametric resolution by introducing optimization parameters as extra-coordinates of the problem, hence the optimization procedure reduces to a simple post-treatment of the multidimensional numerical solution. The aim of this work is to develop a numerical tool dedicated to the optimization of the design of an electromagnetic compression device. This tool should enable to optimize process parameters of the generator and geometrical parameters of the electromagnetic forming device by solving the set of electromagnetic equations in quasistatics. To this end, we take advantage of the Proper Generalized Decomposition (PGD) to perform a parametric resolution. We show solutions computed with a parameterization of the discharged current, and with a parameterization of the geometry considering a multi-layered structure. Finally, an example of optimization procedure is shown on the latter solution, seeking the configuration maximising the radial component of the resultant compression force applied on the part to be formed.