“…Later, it is also used for the simulation of ratcheting [Chaboche (1991)]; McDowell (1992) developed viscoplastic nonlinear kinematic hardening model under thermomechanical cyclic conditions, while Tanaka (1994) developed a viscoplastic constitutive model under non-proportional loading; Ohno and Wang (1993) modified Armstrong-Frederick model [Chaboche (1986)] with dynamic recovery term. Tanaka and Yamada (1993), Abdel-Karim and Ohno (2000) continued with this study especially on the nonlinear kinematic hardening model with steady-state ratchetting, while Chaboche-type nonlinear kinematic hardening models for ratchetting are investigated by McDowell (1995), Kang et al (2001), Kang et al (2002), Kang el al. (2004), Yaguchi and Takahashi (2000), Yaguchi and Takahashi (2005), and Kang et al (2006).…”