A numerical procedure based on the deep drawing simplified inverse approach to optimize material properties of thin sheets

The formability of thin metallic parts obtained by deep drawing can be analysed using finite element codes based on incremental approaches or based on simplified (one step inverse) approaches. The mathematical optimization of process parameters is a more difficult task mainly if a precise incremental approach is considered. The simplified inverse approach has been successfully combined with a mathematical programming technique. In this paper, we present the methodology and some results dealing with the optimization of material properties such as the strain hardening exponent n of the Hollomon constitutive equation and the average anisotropy coefficient r. The Forming Limit Curve (FLC) concept is used to define the objective function. However since the FLC depends on the material parameters, we adopt the theory by Graf and Hosford (1993) based on the growth of material imperfections to define the FLC at each iteration of the optimization loops.