A generalized yield criterion framework with insights into anisotropy and curvature control unrestricted under associated and non-associated flow rules

Forming lightweight sheet metals under complex stress states poses significant challenges in precise process design due to their pronounced plastic anisotropy. To address this, a coupled yield criterion modeling framework is newly proposed, capable of simultaneously capturing the evolution of mechanical properties under diverse loading directions and a wide range of stress states. The modeling framework incorporates flexible analysis techniques to systematically guide the selection of anisotropy and curvature control terms. For validation, a fourth-order polynomial function is adopted as the anisotropic term, while a linearly modified stress-invariant-based function is employed to control curvature of yield locus. Additionally, two material calibration approaches are introduced to analytically determine the anisotropic coefficients, revealing the distinct impacts of stress and deformation anisotropy data on modeling accuracy. The proposed modeling framework and associated yield criteria are applied to both advanced high strength steel and aluminum alloy, with quantitative evaluations of prediction errors in anisotropic yield and flow behavior. Results show that the most effective configuration of the coupled framework involves polynomial-based anisotropic terms and stress-invariant-based curvature terms. The newly developed yield criterion within this framework demonstrates the highest accuracy among all examined models. Furthermore, it is shown that yield criterion calibration should prioritize anisotropy of plastic flow ( r -value) data over stress anisotropy data for improved predictive performance. • Proposed a coupled yield criterion modeling framework under complex stress states • Guided the selection of anisotropy and curvature control terms in the new framework • Introduced an isotropic yield criterion based on the linear modification technique • The new model has the highest accuracy compared to all the yield criteria examined • The calibration of yield criteria should prioritize deformation-induced anisotropy data