We present a simple model for simulating the response of a superelastic shape memory alloy wire based on the thermodynamics of irreversible processes, which can simulate the full thermomechanical response including internal hysteresis loops, at different temperatures, with minimal data input. The key idea is to separate the dissipative response and the elastic response of shape memory alloys using a Gibbs potential based formulation, and then use a Preisach model for the dissipative part of the response. This enables better handling of the features observed in the superelastic response such as those due to changes in temperature and internal hysteresis loops. We compare the predicted response with experiments performed on 0.75 mm NiTi shape memory alloy wires at three different temperatures.

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Shape Memory Alloys are increasingly being used in aeronautic [1], vibration control and seismic applications [2–6]. These applications require models that faithfully represent the full thermomechanical response of SMA wires but which at the same time are simple and fast to implement. In this paper we present a model for the superelastic behavior of Shape Memory Alloys that combines a thermodynamical framework with a Preisach model. This approach allows us to easily account for both stress and strain controlled responses as well as changes in termperature in a simple and straightforward way.

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Modeling superelastic behavior of shape memory alloys (SMA) has received considerable attention due to SMAs ability to recover large strains with associated loading-unloading hysteresis enabling them to find many applications. In this work, a simple mechanics of materials modeling approach for simulating superelastic responses of SMA components under tension and bending loading conditions is developed. Following Doraiswamy, Rao and Srinivasa's 1 approach, the key idea here would be in separating the thermoelastic and the dissipative part of the hysteretic response with a Gibbs potential based formulation which includes both thermal and mechanical loading in the same framework. The dissipative part is then handled by a discrete Preisach model. The model is formulated directly using tensile stress-strain or bending moment-curvature rather than solving for non-homogeneous stress and strains across the specimen cross-sections and then integrating the same especially for bending loading conditions. The model is capable of simulating complex superelastic responses with multiple internal loops and provides an improved treatment for temperature dependence associated with superelastic responses. The model results are verified with experimental results on SMA components like wires and beams at different temperatures.