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.