A thermodynamic model of shape memory alloys involving dynamic functions and constitutive entropy production

The paper develops a thermodynamic model of shape memory alloys in terms of temperature, stress, and martensite fraction. The approach is not traditional. Unlike the wide literature on the subject, the thermodynamic analysis is based on the second law inequality where even the entropy production is given by a proper constitutive function and this proves to be essential for the derivation of the sought evolution equations. The model so obtained accounts for thermal expansion and describes the hysteretic properties of martensite fraction and deformation by means of four constitutive functions viz. the free energy, the entropy production, the dynamic entropy, and the dynamic deformation. The transitions induced by temperature and tensile stress are derived and exemplified in detail. The novelty of the approach is due to a thermodynamic scheme where the austenite-martensite transition is induced by temperature and stress changes.