This article presents a simplified version of Likhachev’s micromechanical model and its integration in ANSYS, a commercial finite element software package used to simulate the response of a structure equipped with shape memory alloy wire actuators controlled by direct Joule heating. The original Likhachev’s formulation is adapted to obtain a model that is easy to characterize, numerically efficient, and general in the sense that it can simulate all the shape memory-related features using the same formulation (superelasticity, shape memory effect, stress generation, etc.). The adapted Likhachev’s formulation is coupled to an electro-thermal model to simulate temporal response of actuators heated by an electrical current. An experimental result obtained with a deformable airfoil powered by shape memory actuators is used to validate the proposed electro-thermo-mechanical model.
Alasty, A. and Shameli, E.2004. ‘‘Dynamic Modeling of a New Varying Stress SMA Actuator for Precise Applications,’’ In: Proceedings of the IEEE International Conference on Mechatronics 2004 - ICM’04, 3-5 June, Istanbul, Turkey, pp. 209-214.
2.
Baril, Y., Brailovski, V. and Terriault, P.2008. ‘‘Fatigue Properties of Superelastic Ti-Ni Filaments Used in Braided Cables for Bone Fixation,’’ In: CIMTEC 2008 - Proceedings of the 3rd International Conference on Smart Materials - Biomedical Applications of Smart Materials, Nanotechnology and Micro/ Nano Engineering, Acireale, Italy, Vol. 57, pp. 235-240.
3.
Benzaoui, H., Lexcellent, C., Chaillet, N., Lang, B. and Bourjault, A.1997. ‘‘Experimental Study and Modeling of a TiNi Shape Memory Alloy Wire Actuator,’’ Journal of Intelligent Material Systems and Structures, 8:619-629.
4.
Brailovski, V., Prokoshkin, S., Terriault, P. and Trochu, F. (eds) 2003. Shape Memory Alloys: Fundamentals, Modeling and Application, Éditions de l’École de technologie Supérieure, Montréal, Canada, 844 pp.
5.
Brailovski, V., Terriault, P., Coutu, D., Georges, T., Morellon, E., Fischer, C. and Bérubé S.2008. ‘‘Morphing Laminar Wing with Flexible Extrados Powered by Shape Memory Alloy Actuators,’’ In: Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2008 (SMASIS2008), Ellicott City, USA, Vol. 1, pp. 915-923.
6.
Chang, B.C., Shaw, J.A. and Ladicola, M.A.2006. ‘‘Thermodynamics of Shape Memory Alloy Wire: Modeling, Experiments, and Application,’’Continuum Mechanics and Thermodynamics, 18:83-118.
7.
Coutu, D., Brailovski, V. and Terriault, P.2010. ‘‘Optimized Design of an Active Extrados Structure for an Experimental Morphing Laminar Wing,’’Aerospace Science and Technology, 14:451-458.
8.
Dong, Y., Boming, Z. and Jun, L.2008. ‘‘A Changeable Aerofoil Actuated by Shape Memory Alloy Springs,’’, Materials Science & Engineering: A (Structural Materials: PropertiesMicrostructure and Processing) , 485:243-250.
9.
Eggleston, B., Poole, R.J.D., Jones, D.J. and Khalid, M.1987. ‘‘Thick Supercritical Airfoil with Low Drag and Natural Laminar Flow,’’ Journal of Aircraft , 24:405-411.
10.
Flores, A., Ahuett, H. and Song, G.2006. ‘‘Design and Experimental Characterization of Flexure Activated by SMA Wires for Microassembly Operations,’’ In: Proceedings of SPIE - The International Society for Optical Engineering - Smart Structures and Materials 2006 - Smart Structures and Integrated Systems, San Diego, USA, p. 6173.
11.
Frautschi, F. and Seelecke, S.2003. ‘‘Finite Element Simulation of Adaptive Aerospace Structures with SMA Actuators,’’ In: Smith, RC (ed.), Proceedings of SPIE - Smart Structures and Materials: Modeling, Signal Processing, and Control, The International Society for Optical Engineering, San Diego, USA, Vol. 5049, pp. 65-75.
12.
Frost, M., Sedlak, P., SIppola, M. and Sittner, P.2010. ‘‘Thermomechanical Model for NiTi Shape Memory Wires,’’Smart Materials and Structures, 19, 094010 (10 pp).
13.
Gao, X., Turner, T.L., Burton, D. and Brinson, L.C.2005. ‘‘Finite Element Analysis of Adaptative-Stiffening and Shape-Control SMA Hybrid Composites,’’ In: Proceedings of SPIE - The International Society for Optical Engineering - Smart Structures and Materials 2005 - Active Materials: Behavior and Mechanics , San Diego, USA, Vol. 5761, pp. 406-416.
14.
Garner, L.G., Wilson, L.N., Lagoudas, D.C. and Rediniotis, O.K.2000. ‘‘Development of a Shape Memory Alloy Actuated Biomimetic Vehicle,’’ Smart Materials and Structures , 9:673-683.
15.
Georges, T., Brailovski, V. and Terriault, P.2009. ‘‘Design of Shape Memory Alloy Actuators for Morphing Laminar Wing with Flexible Extrados,’’Journal of Mechanical Design, 131:091006.
16.
Iata.2009. IATA Technology Roadmap Report, 3rd edn. Online Document . Available at: http://www.iata.org/SiteCollectionDocuments/Documents/Technology_Roadmap_May2009.pdf (accessed date July 7, 2010), 50 pp.
17.
Jayender, J., Patel, R.V., Nikumb, S. and Ostojic, M.2008. ‘‘Modeling and Control of Shape Memory Alloy Actuators,’’ IEEE Transactions on Control Systems Technology, 16:279-287.
18.
Knowles, K.M. and Smith, D.A.1981. ‘‘The Crystallography of the Martensitic Transformation in Equiatomic Nickel Titanium,’’ Acta Metallurgica , 29:101-110.
19.
Lan, C.C. and Yang, Y.N.2009. ‘‘A Computational Design Method for a Shape Memory Alloy Wire Actuated Compliant Finger,’’Journal of Mechanical Design, 131:021009.
20.
Landis, G.A., Jenkins, P., Flatico, J., Oberle, L., Krasowski, M. and Stevenson, S.1996. ‘‘Development of a Mars Dust Characterization Instrument,’’ Planetary and Space Science, 44:1425-1433.
21.
Likhachev, V.A.1995. ‘‘Structure-Analytical Theory of Martensitic Unelasticity,’’Journal de Physique IV, 5:137-142.
22.
Mellor, B.G.1987. ‘‘Engineering Properties of Shape Memory Alloys,’’ In: Proceedings of the Course ‘‘The Science and Technology of Shape Memory Alloys,’’Barcelona, Spain, pp. 334-394.
23.
Nespoli, A., Besseghini, S., Pittaccio, S., Villa, E. and Viscuso, S.2010. ‘‘The High Potential of Shape Memory Alloys in Developing Miniature Mechanical Devices: A Review on Shape Memory Alloy Mini-Actuators,’’Sensors and Actuators A: Physical , 158:149-160.
24.
Otsuka, K. and Wayman, C.M. (eds) 1999. Shape Memory Materials, Cambridge University Press, UK, 284 pp.
25.
Paradis, A., Terriault, P. and Brailosvki, V.2009. ‘‘Modeling of Residual Strain Accumulation of NiTi Shape Memory Alloys Under Uniaxial Cyclic Loading,’’Computational Materials Science, 47:373-383.
26.
Pushtshaenko, O., Oberaigner, E.R., Antretter, T., Fischer, F.D. and Tanaka, K.2002. ‘‘Simulation of the Damping of a Shape Memory Alloy Rod by Using the Likhachev Model,’’ Journal of Intelligent Material Systems and Structures, 13:817-823.
27.
Reynaerts, D. and Van Brussel, H.1994. ‘‘Shape Memory Alloy Based Electrical Actuation for Robotic Applications,’’ In: Proceedings of the First International Conference on Shape Memory and Superelastic Technologies , Pacific Grove, USA, pp. 271-276.
28.
Roh, J.H., Han, J.H. and Lee, I.2006. ‘‘Nonlinear Finite Element Simulation of Shape Adaptive Structures with SMA Strip Actuator,’’ Journal of Intelligent Material Systems and Structures, 17:1007-1022.
29.
Romano, R. and Tannuri, E.A.2009. ‘‘Modeling, Control and Experimental Validation of a Novel Actuator Based on Shape Memory Alloys,’’ Mechatronics , 19:1169-1177.
30.
Spinella, I., Scirè Mammano, G. and Dragoni, E.2009. ‘‘Conceptual Design and Simulation of a compact shape memory actuator for rotary motion,’’Journal of Materials Engineering and Performance, 18:638-648.
31.
Terriault, P., Viens, F. and Brailovski, V.2006. ‘‘Non-isothermal Finite Element Modeling of a Shape Memory Alloy Actuator Using ANSYS,’’ Computational Materials Science, 36:397-410.
32.
Turner, T.L., Buehrle, R.D., Cano, R.J. and Fleming, G.A.2006. ‘‘Modeling, Fabrication, and Testing of a SMA Hybrid Composite Jet Engine Chevron Concept,’’Journal of Intelligent Material Systems and Structures, 17:483-497.
33.
Turner, T.L. and Patel, H.2007. ‘‘Analysis of SMA Hybrid Composite Structures in MSC.Nastran and ABAQUS,’’ Journal of Intelligent Material Systems and Structures, 18:435-447.
Wong, F.C., Boissonneault, O. and Terriault, P.2005. ‘‘Hybrid Micro-macro-mechanical Constitutive Model for Shape-Memory Alloys,’’ In: Proceedings of SPIE - Smart Structures and Materials 2005, San Diego, USA, Vol. 5761, pp. 417-428.
36.
Yang, S. and Seelecke, S.2009. ‘‘FE Analysis of SMA-based Bio-inspired Bone-Joint System,’’Smart Materials and Structures, 18:104020.
37.
Yoo, E.J., Roh, J.H. and Han, J.H.2007. ‘‘Wrinkling Control of Inflatable Booms Using Shape Memory Alloy Wires,’’ Smart Materials and Structures, 16:340-348.
