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Taylor-SPH Method for Viscoplastic Damage Material

Received: 8 May 2015     Accepted: 17 May 2015     Published: 29 May 2015
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Abstract

In this paper, we apply the meshless method Taylor-SPH to solve the propagation of shock wave in viscoplastic material coupled to damage. The equations are written in terms of stress and velocity. Taylor-SPH method is based on the Taylor series expansion of stress and velocity and on the corrected SPH approximation. Numerical stability of the method as a function of the smoothing length and the Courant number is analysed in the elastic case. The Taylor-SPH method is used to simulate localization in a one dimensional viscoplastic damage problem. The numerical results show that the Taylor-SPH method is able to model localization phenomena in viscoplastic damage material without lose of hyperbolicity of partial differential equations.

Published in Applied and Computational Mathematics (Volume 4, Issue 3)
DOI 10.11648/j.acm.20150403.19
Page(s) 162-173
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Taylor-SPH, Meshless, Viscoplastic, Damage, Shock Wave, Stability

References
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[8] C.T. Dyka, R.P. Ingel, An approach for tensile instability in smoothed particle hydrodynamics, Comput. Struct. 57, pp. 573–580, 1995.
[9] M. Mabssout, M. Pastor, A Taylor–Galerkin algorithm for shock wave propagation and strain localization failure of viscoplastic continua, Comput. Methods Appl. Mech. Eng. 192, pp. 955–971, 2003.
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[11] M. I. Herreros, M. Mabssout, A two-steps time discretization scheme using the SPH method for shock wave propagation, Comput. Methods Appl. Mech. Eng. 200, pp. 1833–1845, 2011.
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[13] M. Mabssout, M. I. Herreros, Runge-Kutta vs Taylor-SPH. Two time integration schemes for SPH with application to Soil Dynamics, App. Math. Modelling, 37(5), pp. 3541-3563, 2013.
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  • APA Style

    Hajar Idder, Mokhtar Mabssout. (2015). Taylor-SPH Method for Viscoplastic Damage Material. Applied and Computational Mathematics, 4(3), 162-173. https://doi.org/10.11648/j.acm.20150403.19

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    ACS Style

    Hajar Idder; Mokhtar Mabssout. Taylor-SPH Method for Viscoplastic Damage Material. Appl. Comput. Math. 2015, 4(3), 162-173. doi: 10.11648/j.acm.20150403.19

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    AMA Style

    Hajar Idder, Mokhtar Mabssout. Taylor-SPH Method for Viscoplastic Damage Material. Appl Comput Math. 2015;4(3):162-173. doi: 10.11648/j.acm.20150403.19

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  • @article{10.11648/j.acm.20150403.19,
      author = {Hajar Idder and Mokhtar Mabssout},
      title = {Taylor-SPH Method for Viscoplastic Damage Material},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {3},
      pages = {162-173},
      doi = {10.11648/j.acm.20150403.19},
      url = {https://doi.org/10.11648/j.acm.20150403.19},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150403.19},
      abstract = {In this paper, we apply the meshless method Taylor-SPH to solve the propagation of shock wave in viscoplastic material coupled to damage. The equations are written in terms of stress and velocity. Taylor-SPH method is based on the Taylor series expansion of stress and velocity and on the corrected SPH approximation. Numerical stability of the method as a function of the smoothing length and the Courant number is analysed in the elastic case. The Taylor-SPH method is used to simulate localization in a one dimensional viscoplastic damage problem. The numerical results show that the Taylor-SPH method is able to model localization phenomena in viscoplastic damage material without lose of hyperbolicity of partial differential equations.},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - Taylor-SPH Method for Viscoplastic Damage Material
    AU  - Hajar Idder
    AU  - Mokhtar Mabssout
    Y1  - 2015/05/29
    PY  - 2015
    N1  - https://doi.org/10.11648/j.acm.20150403.19
    DO  - 10.11648/j.acm.20150403.19
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
    SP  - 162
    EP  - 173
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20150403.19
    AB  - In this paper, we apply the meshless method Taylor-SPH to solve the propagation of shock wave in viscoplastic material coupled to damage. The equations are written in terms of stress and velocity. Taylor-SPH method is based on the Taylor series expansion of stress and velocity and on the corrected SPH approximation. Numerical stability of the method as a function of the smoothing length and the Courant number is analysed in the elastic case. The Taylor-SPH method is used to simulate localization in a one dimensional viscoplastic damage problem. The numerical results show that the Taylor-SPH method is able to model localization phenomena in viscoplastic damage material without lose of hyperbolicity of partial differential equations.
    VL  - 4
    IS  - 3
    ER  - 

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Author Information
  • Laboratory of Mechanics and Civil Engineering, Faculty of Science and Technology, Abdelmalek Essaadi University, Tangier, Morocco

  • Laboratory of Mechanics and Civil Engineering, Faculty of Science and Technology, Abdelmalek Essaadi University, Tangier, Morocco

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