Reshaping anisotropic behavior in metallic sheets under complex stress states: Symmetric and asymmetric polynomial models with advanced convexity analysis approach

Fourth-order polynomial-related analytical symmetric and asymmetric anisotropic yield criteria under the non-associated flow rule, are proposed to cover a wider range of stress states. The new model can be directly calibrated using selected experimental data. Additionally, a modified geometry-inspired numerical convexity proof method is developed to demonstrate that the proposed model satisfies the convexity condition. Compared the newly proposed and existing advanced convexity proof methods and yield criteria, and evaluated the applicability and effectiveness of the new framework. The results indicate that the new convexity proof method provides highly accurate convexity identification, consistent with the Hessian matrix method, while maintaining the user-friendliness of the GINCA method. The new symmetric model exhibits the highest accuracy in characterizing the plastic anisotropy of DP490 and AA6016-T4 compared to other investigated yield criteria. Furthermore, the new asymmetric model effectively predicts the strength differential effect under complex stress states. Precise modeling of near-plane strain and pure shear stress states significantly enhances the characterization of stress states in tensile-tensile and tension–compression regions. Applying the anisotropic hardening concept enables continuous capture of the subsequent yielding behavior of metallic sheets.