A trust region algorithm for automatic identification of elasto-viscoplastic model parameters in metallurgical finite element model

Simulation of manufacturing processes, here metal forming, has made major progresses during the last years. The virtual simulation of the manufacturing process being now quite well established, a natural step ahead consists in trying to find automatic procedures to optimize it. Another perspective is also to take care of the influence of the manufacturing constraints upon the design, which is the long term objective of the present research project. It aims at optimizing the design subject to both service constraints (stiffness and strength) and manufacturing constraints. A preliminary stage is to be able to build high fidelity digital models. Complex models require more and more material parameters for behavior laws (e.g. material constitutive and friction laws), which have to be identified numerically from experimental data.
In this material parameter identification process, three steps can be identified. At first, an experimental testing is carried out. The second step consists in building a simulation model of the experiment. Finally, the unknown model parameters are determined to match the experimental data. A standard identification procedure consists in minimizing a given norm (here the Euclidean norm) of the error between the model predictions and the experimental results.
Even if the identification problem is generally quasi-unconstrained, it has the same complexity as structural optimization problems because of the highly nonlinear and implicit character of the functions, which is especially amplified by the large deformation simulation analysis.
In this paper, we use an approach of elastoplastic calculation by finite elements combined with two optimization algorithms: a Levenberg-Marquardt algorithm, which is rather classical in the literature for solving identification problems (see [2]) and a trust-region one (see [1]), which is a rather novel approach at least for structural problems. The results obtained with these two methods are then compared and discussed on two test cases. The first application is an academic test case to validate the identification method. The second one, the compression of a cylinder, takes into account an actual experiment. In this application, the material is assumed to be elasto-viscoplastic and described by a Norton-Hoff behavior law and an isotropic strain hardening law. The parameters to be identified are the coefficients of the Norton-Hoff law.