An implicit algorithm using explicit correctors for the kinematic hardening model with multiple back stresses

This paper presents an efficient mathematical algorithm for a class of non-linear kinematic hardening models with multiple back stresses, as an extension of the implicit integration algorithm for a single back stress hardening model. Explicit formulations for general three-dimensional stress states as well as plane stress and plane strain are given. The new formulation is implemented in a general-purpose finite element code, ABAQUS, and is verified by comparison with the existing formulation for the single back-stress constitutive model. Comparison is also made with the experimental results obtained from a plate containing a circular hole subjected to cyclic loading, demonstrating the validity of new method. Copyright (C) 2001 John Wiley & Sons, Ltd.