Abstract:Shape Memory Alloy (SMA) is a sort of intelligent material systemwidely used in many engineering application fields. The basicmacroscopic response characteristcs are the pseudoelasticity and theshape memory effect at various temperatures and stress levels. Shape memoryalloy constitutive models have developed rapidly and received increasingattention in recent years because of their great potential for the vibrationcontrol of engineering structures. Meanwhile, a series of SMA compositecontitutive models compatible with the developing composite material becomehot topics nowadays and are investigated by many reasearchers.This paper reviews those common SMA constitutive models and newlydeveloped models and classifies them in terms of the mechanical behavior andtheoretical basis. And the characteristics and applicability of the modelsare also compared and analyzed. The developing status of SMA composite constitutive models areintroduced from the point of microcosmic and macroscopical view. Thispaper also presentsan overview to the state of the art of some practical SMAconstitutive models in the fields of active and passive vibration controls,deformation controls and crack diagnoses and control techniques. Finally, thepromising future and engineering applications of SMA constitutive models arediscussed.