Return mapping with a line search method for integrating stress of the distortional hardening law with differential softening

Abstract

ABSTR A C T 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 signifi-cantly improves the accuracy and speed of convergence when the proposed line search method is incor-porated. 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. (c) 2021 Elsevier Ltd. All rights reserved.