Abstract: In order to describe the hardening behavior of metallic materials under nonpropertional cyclic loading, a number of nonproportionality parameters have been proposed10. For some loading paths, the degree of nonpropertional cyclic hardening can be animated by these parameters. But for the paths containing not only the stress relaxation but also the many times unloading per cycle, they do not work well. For instance, these parameters always predicted a higher stress level for the stair-step loading and a low...