Modeling 1-D Isothermal Shape Memory Alloy Microstructure via Legendre Wavelets Collocation Method

  • Xuan He
  • Dan Wang
  • Linxiang WangEmail author
  • Roderick Melnik
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


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.


Legendre 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.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Xuan He
    • 1
  • Dan Wang
    • 1
  • Linxiang Wang
    • 1
    Email author
  • Roderick Melnik
    • 2
  1. 1.State Key Laboratory of Fluid Power and Mechatronic SystemsZhejiang UniversityHangzhouChina
  2. 2.MS2 Discovery Interdisciplinary Research InstituteWilfrid Laurier UniversityWaterlooCanada

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