Application of the virtual fields method to the identification of the homogeneous anisotropic hardening parameters for advanced high strength steels

In the present paper, an inverse problem solution so called the virtual fields method (VFM) is implemented to identify the parameters of the homogeneous anisotropic hardening (HAH) model, a distortional plasticity-based model that describes the material plastic behavior when subjected to strain path changes. The framework of the identification method that combines the formulation of the yield condition, the constitutive stress-strain relation and the principle of virtual work is presented. For validation purpose, the proposed identification method was first attempted on finite element (FE) generated data for a forward-reverse simple shear test to investigate its capability in retrieving the input constitutive parameters. The influence of noise was also evaluated. Then, the identification method was applied to a selection of advanced high strength steel (AHSS), namely DP600, TRIP780 and TWIP980, sheet specimens, subjected to a small number of forward-reverse simple shear cycles. The material constitutive parameters were identified using the VFM based on which shear stress-strain curves were calculated and compared with their experimental counterparts. Good agreement was found between the calculated and the experimental curves despite the larger discrepancies observed in the reverse loading paths. To adjust these discrepancies, the original HAH model was modified with respect to the permanent softening related state variables. After modification, the model was simplified with only one state variable related to permanent softening. It was found that the discrepancies observed in the reverse loading paths were reduced with the modified HAH model.