A comprehensive description for the constitutive behavior of polycrystalline shape memory alloys (SMAs) is proposed based on a two-phase mixture model incorporating the conventional theory of plasticity. An SMA is composed of austenite and martensite phases, and its constitutive behavior should be the combination of the individual behavior of each of the two phases. In the interested ranges of stress and temperature, the behavior of the austenite is assumed to be linearly elastic while that of martensite is assumed to be elastoplastic. The main features of SMAs, such as shape memory effect and pseudoelasticity, can be successfully replicated with the proposed constitutive model. The constitutive behavior of SMA Au-47.5 at.% Cd subjected to uniaxial forward and reverse loading and the pseudoelasticity of Cu-Al-Zn-Mn SMA polycrystal subjected to proportional and nonproportional complex stress or strain histories are simulated and compared with the experimental results.
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