A New Approach to Thermodynamically Consistent Models for SMAs

The paper derives a thermodynamic scheme for SMAs. The new idea of the thermodynamic approach is the formulation of the second law where also the entropy production is given by a constitutive equation. Also by analogy with the usual one-dimensional experimental setting, the paper describes SMAs in a thin parallelepiped form. The body is taken to be subjected to the standard balance equations and the material is characterized by constitutive equations where the temperature, the stress, their time derivatives, and the mass fraction of a phase (martensite) are the variables. The thermodynamic analysis leads to a skeleton surface consisting of equilibrium states and to rate equations governing the evolution of the fields, outside the skeleton surface. It emerges that the rate equations allow a whole account of hysteretic loops induced by temperature or by stress.