An explicit and accurate approach toward simulating plastic-to-pseudoelastic transitions of SMAs under multiple loading and unloading cycles

New finite elastoplastic J2-flow equations are proposed for the purpose of explicitly simulating continuous transitions from plastic to pseudo-elastic effects of SMAs under multiple loading-unloading cycles. Novelties of such models are as follows: (i) New hardening effects are incorporated by introducing interplay between the changing of the yield surface radius and the moving of the yield surface center; (ii) extensive experimental data may be accurately simulated for any given number of loading-unloading cycles; (iii) the complicated task for simulating extensive data may be accomplished by independently fitting certain single-variable functions; and (iv) such single-variable functions may be presented in explicit forms for the purpose of automatically, accurately fitting extensive data, thus bypassing uncertainties and undue complexities usually involved in iteratively solving a coupled system of nonlinear constitutive rate equations toward identifying numerous unknown parameters. Numerical examples for model validation are presented and in good agreement with stress-strain data up to 20 loading-unloading cycles given in literature.