Models for Shape Memory Alloy Behavior: An overview of modeling approaches

Shape memory alloys (SMA) have been known for over five decades and modeling of their response has attracted much attention over the last two decades. Recent increase in the range of applications of these materials has lead to an increased focus on modeling their thermomechanical response. Various approaches ranging from macroscopic phenomenology to microscopic lattice based methods are being pursued to model SMA behavior. Models ranging from simple tools as design aids to complex thermodynamic based models to understand the characteristic martensitic transformation responsible for the shape memory and superelastic response exist. In this report, following a brief introduction to the SMA behavior and the underlying martensitic transformation, an overview of models for SMAs is provided. This is aimed at providing an understanding of the state of the art and also to identify possible future directions. In this review, models are classified both on the basis of the approach and the level (scale) of continuum they address. General methodology of each type of approach is presented briefly followed by a review of the models that fall under that category. Certain liberties are taken in classifying these models to facilitate understanding and thus the present classification is by no means either unique or completely rigorous. Also, while an attempt is made to cover most of the approaches, review of all the models that exist in literature is practically impossible. Finally, summarizing the literature on models for SMAs, several interesting and relevant problems are identified for possible future developments.