Explicit numerical integration algorithm for a class of non-linear kinematic hardening model

An explicit updating algorithm has been developed for the Armstrong-Frederick family of non-linear kinematic hardening model, based on the trapezoidal and the backward Euler integration method. The algorithm provides a computationally efficient method for implementing the non-linear kinematic hardening model in finite element codes. It is shown that the trapezoidal method performs better with the original Armstrong-Frederick rule, while the backward Euler rule provides an improved accuracy to the modified multiple back-stress model that incorporates a weight function for dynamic recovery. Numerical examples are presented to illustrate the performance of the algorithm developed, and a comparison with the experimental observation shows that the modified constitutive model indeed provides a more accurate prediction to the long term mean stress relaxation.