Funct. Mater. 2018; 25 (3): 581-585.

The shape memory alloy (SMA) are widely applied in civil construction. among the various SMAs, except Ni-Ti SMAs, Cu-based SMAs(e.g. Cu-Al-Ni, Cu-Zn-Al and Cu-Al-Mn alloys) are the most potential ones for large-scale industrial applications because of their low cost. SMA have good super-elastic and shape memory effect, and be applied in many engineering field very widely. Many scholars study the constitutive model of the SMA material, and build many models to describe relationship between strain and stress. Four constitutive models are introduced detail and some parameters of the equations is determined by formula, those constitutive model include Tanaka constitutive model, Liang-Rogers constitutive model, Brinson constitutive model and Boyd-Lagoudas constitu-tive model. Each constitutive model is induced detail base on thermos-mechanics, thermodynamics and phase transformation dy-namics and some mechanical assumptions. Other constitutive models are introduced also base on the four constitutive models. Those constitutive model of The SMA material is studied to established foundation for further research.