A new coupled yield criterion focusing on the precise description of anisotropic behavior under broader stress states: Modeling, validation, and convexity analysis

During the forming process, sheet metals are typically subjected to various loading conditions, including uniaxial tension, equi-biaxial tension, near-plane strain, and pure shear. However, most existing yield criteria struggle to accurately capture the plastic anisotropy of materials across various stress states. In response, this work proposes a polynomial-coupled anisotropic yield criterion that accounts for a wider range of stress states, formulated under non-associated flow rule. The anisotropic coefficients of both the yield stress and plastic potential functions are semi-analytically calibrated using selected experimental data, while ensuring convexity requirements are met. Additionally, a novel enhanced geometry-inspired numerical convex analysis approach is introduced to ensure that the proposed model consistently adheres to the convexity condition. The new yield criterion, along with existing advanced models like CFI2023, Min2016, CQN_Chen (non-associated flow rule), and BBC2005, Yld2004-18p, Eyld2000-2d, Poly4*Hosford (associated flow rule), are applied to DP490 and AA6016-T4 sheets. These models are evaluated for predicting plastic work contours and directions of plastic strain rate. Among the eight models, the new criterion offers the most accurate characterization of anisotropic yield and plastic flow for DP490 and AA6016-T4. It effectively captures behavior under various stress states, including uniaxial, equi-biaxial, pure shear, and near-plane strain tension, while anisotropic hardening enhances its ability to capture the subsequent yield behavior.