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Isogeometric analysis of a dynamic thermo-mechanical phase-field model applied to shape memory alloys

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Abstract

This paper focuses on the numerical simulation of martensitic transformations in shape memory alloys (SMAs) using a phase-field model. We developed a dynamic thermo-mechanical model for SMAs, using strain based order parameter, having a bi-directional coupling between structural and thermal physics via strain, strain rate and temperature. The model involves fourth order spatial derivatives representing a domain wall. We propose an isogeometric analysis numerical formulation for straightforward solution to the fourth order differential equations. We present microstructure evolution under different loading conditions and dynamic loading simulations of the evolved microstructures of SMAs of different geometries to illustrate the flexibility, accuracy and stability of our numerical method. The simulation results are in agreement with the numerical and experimental results from the literature.

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Acknowledgments

RD and RM have been supported by NSERC and CRC program, Canada, and JZ by NSERC. HG was partially supported by the European Research Council through the FP7 Ideas Starting Grant program (Project # 307201) and by Consellería de Educación e Ordenación Universitaria (Xunta de Galicia). Their support is gratefully acknowledged.

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Authors and Affiliations

  1. Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, M5S-3G8, Canada

    R. P. Dhote & J. Zu

  2. Department of Applied Mathematics, University of A Coruña, Campus de Elvina, s/n., 15192 , La Coruña, Spain

    H. Gomez

  3. M²NeT Laboratory, Wilfrid Laurier University, 75 University Avenue, Waterloo, ON, N2L-3C5, Canada

    R. N. V. Melnik

  4. Universidad Carlos III de Madrid, Avenida de la Universidad 30, E28911 , Leganes, Spain

    R. N. V. Melnik

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  1. R. P. Dhote
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  2. H. Gomez
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  4. J. Zu
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Correspondence to R. P. Dhote.

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Dhote, R.P., Gomez, H., Melnik, R.N.V. et al. Isogeometric analysis of a dynamic thermo-mechanical phase-field model applied to shape memory alloys. Comput Mech 53, 1235–1250 (2014). https://doi.org/10.1007/s00466-013-0966-0

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  • DOI: https://doi.org/10.1007/s00466-013-0966-0

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