A stress-update algorithm for the recently proposed distortional anisotropic hardening law is developed based on the Newton–Raphson (N–R) algorithm and line search method. The investigated yield function enables the modeling of complex path-dependent flow stress evolutions, particularly the Bauschinger effect, latent hardening/softening, and differential permanent softening. Computationally, the continuous distortion of the yield function under strain-path changes leads to numerical instability, which is overcome by a newly reformulated step-size control method in the line search algorithm. The developed algorithms were implemented in ABAQUS using the closest-point projection method and validated for extra-deep drawing quality and DP780 steel sheets in terms of numerical accuracy and stability under reverse- and cross-loading path changes. The results show that the return-mapping algorithm significantly improves the accuracy and speed of convergence when the proposed line search method is incorporated. In contrast, the conventional N–R based algorithm fails to obtain converged stresses under abrupt loading path changes owing to the sharp corners introduced by the distorted yield surface.

基于 Newton-Raphson (N-R) 算法和线搜索方法，为最近提出的畸变各向异性硬化定律开发了一种应力更新算法。研究的屈服函数能够对复杂的路径相关流动应力演变进行建模，特别是包辛格效应、潜在硬化/软化和差异永久软化。在计算上，屈服函数在应变路径变化下的连续变形会导致数值不稳定，这可以通过线搜索算法中新制定的步长控制方法来克服。开发的算法在 ABAQUS 中使用最近点投影方法实现，并在反向和交叉加载路径变化下的数值精度和稳定性方面验证了超深拉拔质量和 DP780 钢板。结果表明，当采用所提出的线搜索方法时，返回映射算法显着提高了收敛的准确性和速度。相比之下，传统的基于 N-R 的算法由于扭曲的屈服面引入了尖角，因此无法在突然的加载路径变化下获得收敛的应力。