On the thermomechanics of shape memory wires

The thermomechanical behavior of a shape memory wire is modeled based on a theory that takes cognizance of the fact that the body can possess multiple natural configurations [1]. The constitutive equations are developed by first constructing the form of the Helmholtz potential (based on different modes of energy storage), and dissipation mechanisms. The internal energy includes contributions from the strain energy, the latent energy, the interfacial energy and thermal energy. The entropy of the system includes the "entropy jump" associated with the phase transition. The role of the rate of mechanical dissipation as a mechanism for entropy generation and its importance in describing the hysteretic behavior is brought out by considering the difference between hysteretic and non-hysteretic (dissipation-less) behavior. Finally, simple linear or quadratic forms are assumed for the various constitutive functions and the full shape memory response is modeled. A procedure for the determination of the constants is also indicated and the constants for two systems (CuZnAl and NiTi) are calculated from published experimental data (see [2, 3]). The predictions of the theory show remarkable agreement with the experimental data. However, some of the results predicted by the theory are different from the experimental results reported in Huo and Muller [2] We discuss some of the issues regarding this discrepancy and show that there appears to be some internal inconsistency between the experimental data reported in Figure 6 and Figure 9 of Huo and Muller [2] (provided they represent the same sample).