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

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Proceedings of the 1st International Conference on Numerical Modelling in Engineering (NME 2018)

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310027, China

    Xuan He, Dan Wang & Linxiang Wang

  2. MS2 Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON N2L 3L5, Canada

    Roderick Melnik

Authors
  1. Xuan He
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  2. Dan Wang
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  3. Linxiang Wang
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  4. Roderick Melnik
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Corresponding author

Correspondence to Linxiang Wang .

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Editors and Affiliations

  1. Faculty of Engineering and Architecture, Ghent University, Laboratory Soete, Ghent, Belgium

    Magd Abdel Wahab

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He, X., Wang, D., Wang, L., Melnik, R. (2019). Modeling 1-D Isothermal Shape Memory Alloy Microstructure via Legendre Wavelets Collocation Method. In: Abdel Wahab, M. (eds) Proceedings of the 1st International Conference on Numerical Modelling in Engineering . NME 2018. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-2273-0_9

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  • DOI: https://doi.org/10.1007/978-981-13-2273-0_9

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-2272-3

  • Online ISBN: 978-981-13-2273-0

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