Stress update algorithm based on finite difference method and its application to homogenous anisotropic hardening (HAH) model with non-associated flow

Abstract

This paper deals with stress update algorithm based on finite difference method. The proposed algorithm is based on Euler backward method with multi-step return mapping approach. Central difference method was utilized for the approximation of the first and second derivatives of yield function. With the proposed algorithm, it is possible to perform elastic-plastic finite element simulation without any analytical derivatives of yield function. General yield functions including Hill's (1948) and Yld2000-2d, and also the HAH distortion hardening model were implemented to an implicit finite element code (ABAQUS/STANDARD). For the verification purpose, various finite element simulations were performed. With the anisotropic functions, single element loading-unloading and cup-drawing simulation were carried out. The results obtained from the proposed algorithm were compared with the results from analytical derivatives and reference data. The availability of the proposed algorithm for distortional plasticity such as HAH model was evaluated by single element loading-reloading simulations: tension-compression and tension-orthogonal tension. The effectiveness of the proposed algorithm compared to the classical Euler backward method was identified from the simulation results.