Applied and Computational Mathematics

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Taylor-SPH Method for Viscoplastic Damage Material

Received: 08 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.

DOI 10.11648/j.acm.20150403.19
Published in Applied and Computational Mathematics (Volume 4, Issue 3, June 2015)
Page(s) 162-173
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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), 2024. Published by Science Publishing Group

Keywords

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

References
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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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    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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    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://download.sciencepg.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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    T1  - Taylor-SPH Method for Viscoplastic Damage Material
    AU  - Hajar Idder
    AU  - Mokhtar Mabssout
    Y1  - 2015/05/29
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    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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