Data-driven modeling of the Yld2000 yield criterion and its efficient application in numerical simulation - Xiaomin Zhang; Jianzhong Mao; Zhi Cheng (Results in Engineering)
To address the high computational cost resulting from the complex mathematical expressions of traditional high-order yield criteria, this study proposes a data-driven modeling approach for high-order yield criteria aimed at improving computational efficiency in sheet metal forming simulations. Regression models for the yield stress and its first-order derivatives based on the Yld2000–2d yield criterion are developed using several machine learning algorithms, including Random Forest (RF), Multilayer Perceptron (MLP), Histogram-Based Gradient Boosting (HGB), and Support Vector Machine (SVM). The trained models are subsequently integrated into the ABAQUS user material subroutine (UMAT) to enable data-driven yield criterion simulations. This approach not only circumvents the cumbersome partial differential equation solutions inherent in traditional analytical methods but also overcomes the challenges associated with Physics-Informed Neural Networks (PINN), such as boundary condition determination and computational stability. Furthermore, by generating a broadly applicable training dataset, this approach avoids dependence on specific material parameters, thereby exhibiting strong generalizability. The simulation results demonstrate that the data-driven model based on RF exhibits the best overall performance. Compared with traditional analytical computations, the RF-based model achieves approximately a 50 % improvement in computational efficiency while maintaining comparable accuracy, with a maximum error of <0.5 % across different materials and tolerance conditions. In contrast, other algorithmic models exhibited certain deficiencies in either convergence behavior or computational efficiency.