A simple uniaxial model for SMA behavior capable to describe one and two-way shape-memory effect

Shape Memory Alloys (SMA) exhibit a complex thermomechanical behavior induced by the occurrence of phase transformations between Austenite and one or more variants or groups of variants of Martensite. This is reflected at the macroscopic scale by their peculiar functional properties known as: pseudoelasticity, pseudoplasticity, one or two-way shape memory effect. Such properties are nowadays widely known and are exploited in an increasing number of applications including, among others: biomedical devices, aerospace structures, mechanical components, MEMS as well as civil engineering structural elements or devices.Even if the scientific literature abounds with constitutive models for SMA behavior, it seems that only a few of them are capable to take into account, at the same time and in a simple way, all the functional properties. Most of the existing models that describe both the high and low temperature SMA behavior are based on one of the two main choices of the internal variables: either two phase fractions or one phase fraction and the macroscopic transformation strain. This work describes a constitutive model based on a different choice of internal variables: the Martensite fraction and the local transformation strain of the particular type of Martensite active in the RVE. A suitable choice of the free energy function and of the dissipation function leads, within the Ziegler-Green-Naghdi thermomechanical framework, to the construction of a model that takes into account of all the above mentioned SMA properties. This can be seen as a generalization of the models presented in [3] and [4] capable to deal with in a simple and consistent way of Martensite reorientation as well as, in particular, one and two-way shape memory effect.