Modeling 1-D Isothermal Shape Memory Alloy Microstructure via Legendre Wavelets Collocation Method
Microstructure plays a significant role in the research of shape memory alloy (SMA). Using mathematical modeling tools to study microstructures can predict the behaviors of material under applied fields. In the current paper, a 1-D dynamic isothermal model is proposed to simulate the microstructure of SMA via Legendre wavelets collocation method. Because of the good performance of Legendre wavelets basis, this method shows good properties in both precision and stability. This paper gives a detailed numerical algorithm and employs the backward differentiation formula to perform all simulations. Computational simulations are carried out in both static and dynamic systems to study the stress induced phase transformation (PT). Numerical experiments are performed using different grids in this paper to demonstrate the advantages of reduced computing cost of the proposed method. In addition, good convergence of the method is well illustrated by the numerical results. The microstructure of SMA is well captured in the current paper.
KeywordsLegendre wavelets Shape memory alloy Microstructure Phase transformation
This work has been supported by the National Natural Science Foundation of China (Grant No. 51575478 and Grant No. 61571007), the National Sciences and Engineering Research Council (NSERC) of Canada, and the Canada Research Chair Program.
- 2.Vernon, L.B., Vernon, H.M.: Process of manufacturing articles of thermoplastic synthetic resins. In: US Patent 2234993 (1941)Google Scholar
- 3.Wu, M.H., Schetky, L.M.: Industrial applications for shape memory alloys. In: International Conference on Shape Memory and Superelastic Technologies. Pacific Grove, California, USA, pp. 171–182 (2000)Google Scholar
- 4.Leo, D.J., Weddle, C., Naganathan, G., Buckley, S.J.: Vehicular applications of smart material systems. pp. 106–116 (1998)Google Scholar