Accurately and automatically simulating hysteresis loops of shape memory alloys

Toward directly simulating pseudo-elastic effects of shape memory alloys, new elastoplastic equations of von Mises type are proposed by correlating the yield surface radius with the yield surface center, thus establishing a new elastoplasticity model characterized by three coupled quantities for isotropic and anisotropic hardening. Within the framework of conventional macroscopic elastoplasticity, it is demonstrated that the new model can exactly reproduce pseudo-elastic hysteresis effects of shape memory alloys, with no need to characterize any microstructural features of solid–solid phase transitions. To this end, explicit expressions for the three hardening quantities introduced are presented in terms of two single-variable functions. Then, exact closed-form solutions are obtained for the uniaxial stress–strain responses in a loading and a subsequent unloading process, and such responses are shown to give rise to a hysteresis loop shaped just by the foregoing two single-variable functions. As such, hysteresis loops of arbitrary shapes can be simulated in a straightforward and accurate manner simply prescribing two single-variable functions shaping such loops. For the first time, cumbersome and time-consuming procedures both for conducting statistical averaging schemes and for identifying numerous unknown parameters may be bypassed with broad applicability.