Constitutive model of shape memory alloys: Theoretical formulation and experimental validation

The technological application of nickel–titanium shape memory alloys (SMA) requires a constitutive model that can be easily implemented into numerical methods. It should also be possible for the parameters of this model to be obtained experimentally. For these reasons, macroscopic constitutive models have gained ground in SMA designs. To develop a new macroscopic model that encompasses all the characteristics of these materials over the whole range of transformation temperatures, several macromechanical models have been analysed, evaluated and experimentally validated. From the discrepancies observed in these experimental validations, a model is proposed based on a specific critical stress–temperature diagram. In this model, various laws of evolution are formulated for the martensite fraction. Expressions for the elastic modulus and constitutive transformation tensor are also proposed. Experimental validation showed that this model predicts the behaviour of the material better than the previous models.