2022 Volume 2022 Pages 20220001
The objective of this study is to improve numerical stability of an elastic-plastic model with memory surface that realizes various hardening behaviors under different ranges of cyclic loading by combination between a primal-dual interior point method and a return mapping algorithm. The primal-dual interior point method allows us to smoothly optimize a minimization problem with inequality constraints such as a yield function and memory surface. More specifically, the inequality condition is replaced with the equal condition by introducing the slack variable and the duality gap is gradually reduced by employing the path-following method. On the other hand, the primal-dual interior method could require bigger computational cost than the conventional return mapping method because of the increase of the unknown variable and the path-following method. Thus, an implicit solution for an elastic-plastic model with the memory surface is proposed by combining with the primal-dual interior point method and the return-mapping algorithm. In addition to the numerical cost, the numerical accuracy of the primal-dual interior point method is evaluated by the comparison with the conventional return mapping algorithm by an iso-error map that has been often applied for the conventional elastic-plastic models. After then, the capability of the proposed implicit method for an elastic-plastic model with the memory surface is demonstrated throughout the simple numerical examples.
