New micromechanical estimates of the interaction energy for shape memory alloys modeled by a two-phases microstructure

The interaction energy is a fundamental ingredient in the modeling of the macroscopic behavior of shape memory alloys and several attempts have been carried out to derive explicit formulas for it by micromechanical methods. The available models vary in sophistication according to the level of detail in the description of the underlying microstructure. There is, however, a common issue with most micromechanical estimates: they tend to overestimate the values of the interaction energy. While various solutions to this problem can be envisaged in the framework of multi-variant models by enriching the description of the microstructure, it seems that similar remedies are not yet available in the two-phases setting. In this work the quantitative relevance of this effect is evaluated, in a sample case, showing that it may lead to violations of the second law of thermodynamics. A new class of micromechanical estimates based on a two-phases microstructure is then proposed and used to model, in an overall way, the secondary accommodation phenomena that take place around product phase regions. The proposed expressions for the interaction energy turn out to yield physically plausible values, consistent with the thermodynamical bounds