A two-phase mixture model for SMAs and application to the analysis for pseudoelasticity of a SMA polycrystal

Shape memory alloys (SMAs) are composed of austenite and martensite and the volume fraction of each phase evolves during thermomechanical loading histories. The constitutive behavior of a SMA is substantially the combination of the individual behavior of each of the two phases. Based on mixture theory, a two-phase mixture constitutive model is proposed, in which the behavior of the austenite is assumed to be linearly elastic while that of the martensite is elastoplastic. The pseudoelastic behavior of a Cu-Al-Zn-Mn polycrystal subjected to proportional and complex stress or strain histories is analysed, and the main features are well replicated. The proposed model is physically distinct, simple and can easily be applied in practical engineering problems.