Inverse Methods Applied to Metal Forming Processes

Abstract

This paper presents some inverse methods for non-steady forming problems, and more precisely in the frame of parameter identification and shape optimisation. In any case, the main issue is to carry out the sensitivity analysis, i.e. to differentiate the problem equations. Two alternatives are studied: the direct differentiation and the adjoint state methods. The direct differentiation method was presented in earlier papers, so it is briefly recalled here. The emphasis is rather put on the accuracy of the derivative calculations, for problems with remeshings and transfers of variables. The adjoint state method being more frequently used for steady-state problems, it is described here in the frame of non-steady forming processes. Some practical details for an efficient implementation are given. The direct differentiation method is applied to shape optimisation problems, the preform design in two-steps forging processes. Different studied objective functions are recalled. An industrial example of automatic design shows the efficiency of these inverse methods in non-steady metal forming.