Shape memory alloy actuator wires undergo a significant (∼4%) contraction and a corresponding change in resistance because of a temperature- and load-induced phase transformation. When a restoring force such as a pre-stretched bias spring is placed in series with a shape memory alloy wire, the system becomes an actuator that can generate a repeatable force. Simultaneously, the resistance of the wire can be correlated to strain and enable self-sensing, eliminating the need for external feedback sensors. The self-sensing task, however, is complicated in applications requiring multiple coupled wires, for example, advanced two-dimensional or three-dimensional positioning. The presence of coupled (passive or active) actuator wires with nonlinear, hysteretic force–displacement characteristics has a strong impact on an individual wire’s resistance behavior that has not been systematically studied to date. This article expands upon previous work that studied a single-shape memory alloy–spring system by adding a second opposing shape memory alloy wire and focusing on the resistance to strain mapping that is crucial for self-sensing applications. Systematic stress–strain and resistance–strain experiments are presented alongside physics-based modeling results that help to identify several sources of hysteresis in the resistance–strain behavior and facilitate intelligent calibration schemes for multifunctional self-sensing and actuation applications.
AchenbachM (1989) A model for an alloy with shape memory. International Journal of Plasticity5: 371–395.
2.
AntonucciVFaiellaGGiordanoM. (2007) Electrical resistivity study and characterization during NiTi phase transformations. Thermochimica Acta462: 64–69.
3.
BrinsonLC (1993) One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. Journal of Intelligent Material Systems and Structures4: 229–242.
4.
BungetGSeeleckeS (2008) BATMAV: a biologically-inspired micro-air vehicle for flapping flight—kinematic modeling. In: Proceedings of SPIE—active and passive smart structures and integrated systems, San Diego, California, 9–13 March 2008.
5.
CalkinsFTMabeJ (2008) Shape memory alloy based morphing aerostructures. Journal of Mechanical Design132.
6.
CarballoMPuZJWuKH (1995) Variation of electrical resistance and the elastic modulus of shape memory alloys under different loading and temperature conditions. Journal of Intelligent Material Systems and Structures6: 557–565.
7.
ChemiskyYDuvalAPatoorE. (2011) Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation. Mechanics of Materials43: 207–213.
8.
ChurchillCBShawJA (2008) Shakedown response of conditioned shape memory alloy wire. Behavior and Mechanics of Multifunctional and Composite Materials 6928.
9.
CrewsJH (2011) Development of a shape memory alloy actuated robotic catheter for endocardial ablation: modeling, design optimization, and control. Doctoral Dissertation, North Carolina State University, Raleigh, NC.
10.
CuiDSongGHongnanL (2010) Modeling the electrical resistance of shape memory alloy wires. Smart Materials and Structures19.
FurstSJSeeleckeS (2011) Experimental validation of different methods for controlling a flexible nozzle using embedded SMA wires as both positioning actuator and sensor. In: Proceedings of SPIE—active and passive smart structures and integrated systems, San Diego, California, 9–13 March 2011.
13.
FurstSJSeeleckeS (2012) Modeling and experimental characterization of the stress, strain, and resistance of SMA actuator wires with controlled power input. Journal of Intelligent Material Systems and Structures23(11): 1233–1247.
14.
FurstSJCrewsJHSeeleckeS (2012) Numerical and experimental analysis of inhomogeneities in SMA wires induced by thermal boundary conditions. Continuum Mechanics and Thermodynamics. 24(4–6): 485–504.
15.
FurstSJHangekarRSeeleckeS (2010) Practical implementation of resistance feedback measurement for position control of a flexible smart inhaler nozzle. In: Proceedings of the ASME conference on smart materials, adaptive structures and intelligent systems, Philadelphia, PA, 28 September – 1 October 2010.
16.
GeorgesTBrailovskiVTerriaultP (2012) Characterization and design of antagonistic shape memory alloy actuators. Smart Materials and Structures21(3).
17.
GravattLMMabeJHCalkinsFT. (2010) Characterization of varied geometry shape memory alloy beams. In: Proceedings of SPIE - The International Society for Optical Engineering, San Diego, California, 7 - 11 March 2010, v 7645.
18.
HeintzeO (2004) A computationally efficient free energy model for shape memory alloys—experiments and theory. Doctoral Dissertation, North Carolina State University, Raleigh, NC.
19.
HuoY (1989) A mathematical model for the hysteresis in shape memory alloys. Continuum Mechanics and Thermodynamics1: 283–303.
20.
JayenderJAzizianMPatelRV (2008) Autonomous image-guided robot-assisted active catheter insertion. IEEE Transactions on Robotics24(4): 858–871.
21.
KleinsteuerCZhangZLiZ. (2008) A new methodology for targeting drug-aerosols in the human respiratory system. International Journal of Heat and Mass Transfer51(23–24): 5578–5589.
22.
KoJJunMBGilardiG. (2011) Fuzzy PWM-PID control of cocontracting antagonistic shape memory alloy muscle pairs in an artificial finger. Mechatronics21(7): 1190–1202.
23.
LagoudasD (2008) Shape Memory Alloys: Modeling and Engineering Applications. New York: Springer.
24.
LanCCFanC (2010) An accurate self-sensing method for the control of shape memory alloy actuated flexures. Sensors and Actuators A: Physical163: 323–332.
25.
LanCCYangYN (2009) A computational design method for a shape memory alloy actuated compliant finger. Journal of Mechanical Design131: 21009-1–21009-9.
26.
LangelaarMVan KeulenF (2008) Modeling of shape memory alloy shells for design optimization. Computers & Structures86: 955–963.
27.
LiHMaoCXOuJP (2005) Strain self-sensing property and strain rate dependent constitutive model of austenitic shape memory alloy: experiment and theory. Journal of Materials in Civil Engineering17(6): 676–685.
28.
LiQ (2006) Modeling and finite element analysis of smart materials. Doctoral Dissertation, North Carolina State University, Raleigh, NC.
29.
MassadJESmithRC (2005) A homogenized free energy model for hysteresis in thin-film shape memory alloys. Thin Solid Films489(1–2): 266–290.
MoallemMTabriziVA (2009) Tracking control of an antagonistic shape memory alloy pair. IEEE Transactions on Control Systems Technology17(1): 184–190.
32.
MullerIWilmanskiK (1980) A model for a pseudoelastic body. Il Nuovo Cimento della societa Italiana di Fisica: B57: 284–318.
33.
PausleyMESeeleckeS (2008) Multifunctional SMA-based smart inhaler system for improved aerosol drug deliver—design and fabrication. In: Proceedings of SPIE—active and passive smart structures and integrated systems, San Diego, California, 9 – 13 March 2008.
34.
RichterFKastnerOEggelerG (2009) Implementation of the Muller-Achenbach-Seelecke model for shape memory alloys in ABAQUS. Journal of Materials Engineering and Performance18(5–6): 626–630.
35.
SarsVDHaliyoSSzewczykJ (2010) A practical approach to the design and control of active endoscopes. Mechatronics20(2): 252–264.
36.
SeeleckeS (2002) Modeling the dynamic behavior of shape memory alloys. International Journal of Non-Linear Mechanics37: 1363–1374.
37.
SeeleckeSMullerI (2004) Shape memory alloy actuators in smart structures: modeling and simulation. Applied Mechanics Reviews57(1): 23–46.
38.
SinghKSirohiJChopraI (2003) An improved shape memory alloy actuator for rotor blade tracking. Journal of Intelligent Material Systems and Structures14: 767–786.
39.
SmithRC (2005) Smart Material Systems: Model Development. Philadelphia, PA: Society for Industrial and Applied Mathematics.
40.
SmithRCSeeleckeSZoubeidaO. (2003) A free energy model for hysteresis in ferroelectric materials. Journal of Intelligent Material Systems and Structures14: 719–739.
41.
SoflaAYNElzeyDMWadleyHNG (2008a) Cyclic degradation of antagonistic shape memory actuated structures. Smart Materials and Structures17(2).
42.
SoflaAYNElzeyDMWadleyHNG (2008b) Two-way antagonistic shape actuation based on the one-way shape memory effect. Journal of Intelligent Material Systems and Structures19(9): 1017–1027.
43.
StepanLLLeviDSCarmanGP (2005) A thin-film nitinol heart valve. Journal of Biomechanical Engineering: Transactions of the ASME127: 75–81.
44.
VeeramaniASBucknerGDOwenSE. (2008) Modeling the dynamic behavior of a shape memory alloy actuated catheter. Smart Materials and Structures17.
45.
WuXDFanYZWuJS (2000) A study on the variations of the electrical resistance for NiTi shape memory alloy wires during the thermo-mechanical loading. Materials & Design21(6): 574–578.
46.
WuXDWuJWangZ (1999) The variation of electrical resistance of near stoichiometric NiTi during thermo-mechanic procedures. Smart Materials and Structures8: 574–578.
47.
ZhangJYinY (2012) SMA-based bionic integration design of self-sensor–actuator-structure for artificial skeletal muscle. Sensors and Actuators A: Physical181: 94–102.
48.
ZhangZKleinstreuerCKimCS (2009) Comparison of analytical and CFD models with regard to micron particle deposition in a human 16-generation tracheobronchial airway model. Journal of Aerosol Science40(1): 16–28.
