The Effects of Geometric Parameters Under Small and Large Deformations on Dissipative Performance of Shape Memory Alloy Helical Springs

Document Type : Original Research Paper


Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran.


This paper presents an investigation into shape memory alloy (SMA) springs considering the effects of geometry changes under small as well as large deformations. Helical springs were fabricated by shape setting of NiTi wires through heat treatment. The products exhibited pseudoelasticity at the ambient temperature, and their force-displacement responses were examined by performing simple tension tests. A model was further proposed to study tension and compression of SMA springs, and it was shown that the consequences of geometrical changes in tension and compression of springs are different. The numerical results of large and small deformation models were verified by experimental tensile results. In order to design a spring with maximum dissipative performance, a designer has three geometric parameters to set: wire diameter, spring diameter, and the number of active coils. The influences of these parameters on dissipated energy were studied in both displacement- and force-control loadings, and a framework for designing SMA springs with the purpose of achieving maximum applicable dissipation was at last developed.


[1] K. Yamauchi, I. Ohkata, K. Tsuchiya, S. Miyazaki, Shape memory and superelastic alloys: Applications and technologies, Elsevier, (2011).
[2] L. Janke, C. Czaderski, M. Motavalli, J. Ruth, Applications of shape memory alloys in civil engineering structures-overview, limits and new ideas, Mater. Struct., 38(5) (2005) 578-592.
[3] A. Saeedi, M.M. Shokrieh, Effect of shape memory alloy wires on the enhancement of fracture behavior of epoxy polymer, Polym. Test., 64 (2017) 221-228.
[4] S.W. Kim, J.G. Lee, S. An, M. Cho, K.J. Cho, A large-stroke shape memory alloy spring actuator using double-coil configuration, Smart Mater. Struct., 24(9) (2015) 095014.
[5] D. Patil, G. Song, A review of shape memory material’s applications in the offshore oil and gas industry, Smart Mater. Struct., 26(9) (2017) 093002.
[6] P. Zhuang, S. Xue, P. Nie, W. Wang, Experimental and numerical study on hysteretic performance of SMA spring-friction bearings, Earthq. Eng. Eng. Vib., 15(4) (2016) 597-609.
[7] G. Attanasi, F. Auricchio, M. Urbano, Theoretical and experimental investigation on SMA superelastic springs, J. Mater. Eng. Perform., 20(4-5) (2011) 706-711.
[8] M.A. Savi, P.M.C. Pacheco, M.S. Garcia, R.A. Aguiar, L.F.G. de Souza, R.B. Da Hora, Nonlinear geometric influence on the mechanical behavior of shape memory alloy helical springs, Smart Mater. Struct., 24(3) (2015) 035012.
[9] J. Wang, Z. Moumni, W. Zhang, W. Zaki, A thermomechanically coupled finite deformation constitutive model for shape memory alloys based on Hencky strain, Int. J. Eng. Sci., 117 (2017) 51-77.
[10] S.M. An, J. Ryu, M. Cho, K.J. Cho, Engineering design framework for a shape memory alloy coil spring actuator using a static two-state model, Smart Mater. Struct., 21(5) (2012) 055009.
[11] S. Enemark, I.F. Santos, M.A. Savi, Modelling, characterisation and uncertainties of stabilised pseudoelastic shape memory alloy helical springs, J. Intell. Mater. Syst. Struct., 27(20) (2016) 2721-2743.
[12] M.M. Khan, D.C. Lagoudas, Modeling of shape memory alloy pseudoelastic spring elements using Preisach model for passive vibration isolation, Smart Mater. Struct., 4693 (2002) 336-348.
[13] B. Heidari, M. Kadkhodaei, M. Barati, F. Karimzadeh, Fabrication and modeling of shape memory alloy springs, Smart Mater. Struct., 25(12) (2016) 125003.
[14] F. Jahanbazi, Experimental and Theoretical Study of Superelastic Shape Memory Alloy Coil Springs, Master Thesis, Isfahan University of Technology, (2017).
[15] L.C. Brinson, One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable, J. Intell. Mater. Syst. Struct., 4(2) (1993) 229-242.
[16] J.H. Chung, J.S. Heo, J.J. Lee, Implementation strategy for the dual transformation region in the Brinson SMA constitutive model, Smart Mater. Struct., 16(1) (2006) N1-N5.
[17] A.M. Wahl, Mechanical springs, Penton Publishing Company, (1944).
[18] S. Sameallah, M. Kadkhodaei, V. Legrand, L. Saint-Sulpice, S.A. Chirani, Direct numerical determination of stabilized dissipated energy of shape memory alloys under cyclic tensile loadings, J. Intell. Mater. Syst. Struct., 26(16) (2015) 2137-2150.
[19] M. Hesami, L. Pino, L. Saint-Sulpice, V. Legrand, M. Kadkhodaei, S. Arbab Chirani, S. Calloch, Rotary bending fatigue analysis of shape memory alloys, J. Intell. Mater. Syst. Struct., 29(6) (2018) 1183-1195.