Inverse analysis of thermomechanical upsetting tests using gradient method with semi-analytical derivatives
Résumé
The starting point of this work is the need of precise and correct input data for material forming codes. The use of these codes as a direct model for inverse analysis of the processes permits to extend the validity range of the thermomechanical parameters in terms of temperature, strain and strain rate. The identification software was developed on the basis of the 2D and of a 3D finite element code (FORGE2((R)) and FORGE3((R))) simulating forming processes and using a thermo-elasto-viscoplastic behaviour. The optimisation problem is based on a Gauss Newton algorithm and necessitates the evaluation of the derivatives of the cost function and of the sensitivity matrix to solve the system. Different methods are proposed to evaluate these derivatives. We have studied deeply analytical evaluation, finite difference techniques and recently semi-analytical derivatives. In this paper we present the main feature of the semi-analytical derivatives and the comparison with numerical ones on the parameter identification during upsetting tests. The semi-analytical method of sensitivity analysis for inverse problems is very attractive thanks to the compromise between computational time and ease of derivatives evaluation. Especially for parameter identification in material forming domain, this technique seems to be promising.