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

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