Matlab® Algorithm to Simulate the Dynamic Behavior of an NiTi Alloy through Ansys® APDLTM Models


In recent years, technological advances related with the so-called intelligent materials have been exploited for problem solving in many engineering fields. In this regard, shape memory alloys (SMA) seem suitable for medical and engineering applications and many others. These alloys have the ability to return to the original form after an apparently plastic deformation by applying heat and the also ability to perform phase changes with voltage variations under a specific temperature. These properties allow the development of a hysteretic loop with energy dissipation, which can be used as  a damping element in a vibratory system. In this paper, a MATLAB algorithm was developed to create an interface with the Ansys® APDLTM software that simulate the dynamic behavior of a SMA. The software is capable to obtain the cyclical behavior of a vibratory mechanical system based on the energy dissipation properties of the SMA. The results show that the free vibration of a mass-damper (alloy) system presents the energy dissipation related in magnitude with the area of the hysteresis loop until the deformation caused by the motion which does not correspond to a voltage required to initiate the (direct) phase transformation of the material, thus reducing the displacement to a constant level.

Keywords: SMA, ANSYS APDLTM, Matlab

[1] Lagoudas, D. C. (2008). Shape Memory Alloys- Modeling and Engineering Applications. New York: Springer.

[2] Sun, Y., Luo, J., Zhu, J. (2018). Phase field study of the microstructure evolution and thermomechanical properties of polycrystalline shape memory alloys: Grain size effect and rate effect. Computational Materials Science, vol. 145, pp.252-262.

[3] Silva, M. A. (2018). Simulação do comportamento dinâmico de sistemas mecânicos vibratórios amortecidos pelo comportamento pseudo-elástico de ligas com memória de forma. Dissertação, Instituto Politécnico de Bragança.

[4] Lobo, P. S., Almeida, J., Guerreiro, L. (2015). Semi-active damping device based on superelastic shape memory alloys. Structures, vol. 3, pp. 1-12.

[5] Qian, H., Li, H., Song, G. (2016). Experimental investigations of building structure with a superelastic shape memory alloy friction damper subject to seismic loads. Smart Materials and Structures, vol. 25.

[6] Li, H. N., Huang, Z., Fu, X., Li, G. (2018). A re-centering deformation-amplified shape memory alloy damper for mitigating seismic response of building structures. Struct Control Health Monit., vol. 25.

[7] Morais, J., Morais, P. G., Santos, C., Costa, A. C., Candeias, P. (2017). Shape memory alloy based dampers for earthquake response mitigation. Procedia Structural Integrity, vol. 5, pp. 705-712.

[8] Speicher, M. S., DesRoches, R., Leon, R. T., Investigation of an articulated quadrilateral bracing system utilizing shape memory alloys. Journal of Constructional Steel Research, vol. 130, pp. 65-78.

[9] Garafolo, N. G., McHugh, G. R. (2018). Mitigation of flutter vibration using embedded shape memory alloys. Journal of Fluids and Structures, vol. 76, pp. 592-605.

[10] Brinson, L. C. (1993). One-dimensional constitutive behavior of shape memory alloys: Thermomechani- cal derivation with non-constant material functions and redefined martensite internal variable. Journal of Intelligent Material Systems and Structures, vol. 4.

[11] Tanaka, K., Kobayashi, S., Sato, Y. (1986). Thermomechanics of transformation pseudoelasticity and shape memory effect in alloys. International Journal of Plasticity, vol. 2, pp. 59-72.

[12] Auricchio, F. (2001). A robust integration-algorithm for a finite-strain shape-memory-alloy superelastic model. International Journal of Plasticity, vol. 17, pp. 971-990.

[13] Pasquali, P. R. Z. (2008). Análise limite de estruturas através de uma formulação em elasticidade não- linear. Dissertação, Universidade Federal do Rio Grande do Sul.

[14] RAO, S. S. (2011). Mechanical Vibrations. Prentice Hall: Pearson.

[15] Kelly, S. G. (2000). Fundamentals of Mechanical Vibrations. Europe: McGraw Hill.

[16] Razavilar, R., Fathi, Al., Dardel, M., Hadi, J. A. (2018). Dynamic analysis of a shape memory alloy beam with pseudoelastic behavior. Journal of Intelligent Material Systems and Structures, vol. 115.

[17] Moraes, Y. J. O., Silva, A. A., Rodrigues, M. C., et al (2018). Dynamical analysis applied to passive control of vibrations in a structural model incorporating SMA-SE coil springs. Advances in Materials Science and Engineering.

[18] Tobushi, H., Iwanaga, H., Tanaka, et al (1992). Stress-strain-temperature relationships of TiNi shape memory alloy suitable for thermomechanical cycling. JSME International Journal, Series I, vol 35, issue 3.

[19] Wang, B. and Zhu, S. (2018). Cyclic tension-compression behavior of superelastic shape memory alloy bars with buckling-restrained devices. Construction and Building Materials, vol. 186, pp. 103-113.

[20] Toi, Y. and He, J. (2010). Dynamic and cyclic response simulation of shape memory alloy devices. ICCSA 2010, Part III, Lecture Notes in Computer Science, vol. 6018, pp. 498-510.

[21] Paiva, A. and Savi, M. A. (1999). Sobre os modelos constitutivos com cinética de transformação assumida para ligas com memoria de forma. XV Congresso Brasileiro de Engenharia Mecânica. Águas de Lindóia: UNICAMP.

[22] SHARCNET – Shared Hierarchical Academic Research Computing Network, 4.14. Shape memory alloy (SMA). (03/11/2018)