Estimation of constitutive parameters using an inverse method coupled to a 3D finite element software

Forming process simulations require a precise knowledge of the input material parameters. These parameters are usually estimated from mechanical tests. The classical analysis of these tests are usually based on a few assumptions: material flow homogeneity, isothermal conditions, etc. But in some cases with strain localisation or self-heating, these assumptions overestimate material strength. Analysis techniques using inverse methods are then good alternatives. This paper deals with the estimation of mechanical parameters using an inverse method. The direct model is a 3D forming process simulation software (FORGE3®). The numerical formulation is based on a mixed finite element method using two unknowns, the velocity and the pressure. The tetrahedron element is linear in velocity and pressure and the thermal problem is solved using a linear element. The inverse problem associated with the estimation of mechanical parameters is expressed as a least square problem. The aim is to obtain output of the direct model which fits experimental data measured during the mechanical test. The optimisation problem is solved using a Gauss–Newton algorithm. At the end of the optimisation, an estimation of confidence intervals is done. A Gauss–Newton algorithm requires the computation of the derivatives of the output with respect to the parameters to be identified. In this work, a semi-analytical differentiation is performed. The proposed method is first validated on artificial experimental data obtained from direct simulations of hot uniaxial compressions for a viscoplastic cylinder. The confidence interval is provided by the algorithm for different configurations with additional random noise. Finally a real steel compression test is analysed to provide parameters for the Norton–Hoff viscoplastic law.