“…The ratcheting deformation of SMAs during cycling has been widely investigated experimentally by researchers in the last decade, including strain-controlled [ 36 , 37 , 38 , 39 ] and stress-controlled [ 17 , 40 , 41 , 42 , 43 ] cyclic loading tests. According to the experimental observations, several phenomenological constitutive models for SMAs have been developed to successfully predict ratcheting deformation during multiple cycles [ 44 , 45 , 46 , 47 , 48 , 49 , 50 ]. Tanaka et al [ 44 ] introduced three internal variables into a macroscopic theoretical framework to interpret the hysteresis behavior of SMAs during thermomechanical cyclic loadings, and they also analyzed the subloops due to the incomplete transformations of the SMAs.…”