Inverse problems in finite element simulation of metal forming processes

The inverse problems arising from the finite element simulation of metal forming processes are discussed. A particular class of problems concerning optimization of industrial forming processes is also described. Shape optimization of the die profile in extrusion and of the pre-forming dies in forging using numerical simulations and trials and errors are considered for solving these problems. Regarding the shape optimization problem of the preforming tool, it is shown that satisfactory solutions can be obtained after a reduced number of iterations of the optimization procedure.