“…Non-proportional loading histories induced greater hardening than those of proportional and resulted in slower rates in the ratcheting progress over multiaxial stress cycles [37]. To study the influence of non-proportionality, complex loading paths, and loading steps on ratcheting response of materials, several ratcheting experiments have been conducted [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. Hassan et al [5,8,43] investigated the capability of kinematic hardening rules in ratcheting simulation of materials under multiaxial stress cycles and reported that the effect of non-proportionality was yet to be fully addressed.…”