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Modelling the constitutive behaviour of martensite and austenite in shape memory alloys using closed-form analytical continuous equations

: Pai, A.; Niendorf, T.; Krooss, P.; Koke, I.; Traechtler, A.; Schaper, M.


Araujo, A.L.:
Smart Structures and Materials : Selected Papers from the 7th ECCOMAS Thematic Conference on Smart Structures and Materials; held from 3 to 6 June 2015 at Ponta Delgada, Azores, Portugal
Cham: Springer International Publishing, 2017 (Computational methods in applied sciences 43)
ISBN: 978-3-319-44505-2 (Print)
ISBN: 978-3-319-44507-6 (Online)
Thematic Conference on Smart Structures and Materials (SMART) <7, 2015, Ponta Delgada>
Fraunhofer IPT ()

Shape Memory Alloy (SMA) actuators capable of precise position control are faced with numerous challenges attributed mostly to the extreme non-linearities of such alloys. The development of control strategies for such actuators is alleviated by the use models incorporating these non-linearities. Such models should, however, among other characteristics, be real-time capable in order to bring reasonable benefits. This work presents a novel constitutive phenomenological model for martensite and austenite. The model is based entirely on continuous differentiable analytical equations and these closed-form equations are capable of depicting the smooth curvatures observed in the SMA stress-strain characteristic with few and easy to identify physical parameters. They can describe shape changes in both SMA phases (martensite or austenite) when subjected to monotonic as well as cyclic loading, including minor loop behaviour. The model is validated by stress-strain experiments and the results show outstanding correlation with experimental data. Since the model is based on simple closed-form equations, it is extremely computational efficient and can build the foundation for the development of real-time capable SMA models for control algorithms.