Analytical anisotropic hardening extension of a differential hardening yield function for strength modelling under various stress states with non-associated flow rule by a new linear transformation tensor

The general \({I}_{1}{J}_{2}{J}_{3}\) yield function (Lou et al. in Int J Plast 158:103414, 33) is extended to an analytically anisotropic form by using a newly proposed five-parameter linear transformation tensor based on the work of Barlat et al. Int J Plast 7:693–712, 7). The anisotropic parameters are analytically calculated so that the proposed yield function can model both differential hardening at various stress states and anisotropic hardening along different loading directions. The extended anisotropic form is applied to characterize the strain hardening behavior of metals of three different polycrystal structures, including AA7075 T6 aluminium, QP1180 steel, and AZ31 magnesium. The results show that the extended anisotropic form is capable of precisely modelling both the differential and anisotropic hardening for the studied metals under various stress states. The proposed function is also applied to a high strength steel QP980 (Hou et al. J Mater Process Technol 290:116979, 17) to validate the capability of the proposed model for the modeling of strength differential (SD) effect between uniaxial tension and compression and its evolution with respect to plastic strain. The results show that the proposed function is capable of predicting the SD effect between uniaxial tension and compression with very high accuracy along RD, DD and TD. Convexity analysis is conducted during yield surface evolution by a newly proposed geometry-inspired numerical convex analysis method to ensure the yield surface convexity during significant change of yield surfaces.