Numerical integration method for kinematic hardening rules with partial activation of dynamic recovery term

In order to express steady state ratcheting, Abdel-Karim and Ohno formulated kinematic hardening rules on the assumption that dynamic recovery term of back stress is partially activated before it reaches its critical value. These rules have a feature that only the projection of plastic strain rate into the direction of back stress contributes to the dynamic recovery. They are in contrast with the other rules in which either/both accumulated plastic strain rate or/and plastic strain rate enters into the dynamic recovery term. In this paper, another feature, which has not been investigated by Abdel-Karim and Ohno, is introduced. Discussing this feature, characterized by decomposition of back stress into radial and tangential components, a numerical integration method based on radial-return mapping using radial components only is developed. This method consists of a trial predictor and final corrector depending on the current state of back stress and plastic strain increment. The applicability of the method is examined carefully and critically. It is shown that this method is effective and its accuracy is indistinguishable to the radial-return method for elastic-perfectly plastic materials.