Taylor-SPH Method for Viscoplastic Damage Material

Hajar Idder; Mokhtar Mabssout

doi:doi:10.11648/j.acm.20150403.19

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Taylor-SPH Method for Viscoplastic Damage Material

Hajar Idder, Mokhtar Mabssout

Published in Applied and Computational Mathematics (Volume 4, Issue 3)

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), 2024. Published by Science Publishing Group

Keywords

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

References

[1]	L.B. Lucy, A numerical approach to the testing of fusion process, Astronomical Journal, 82, pp. 1013-1024, 1977.
[2]	R.A. Gingold, J.J, Monaghan, Smoothed particles hydrodynamics: Theory and application to nonspherical stars, Monthly Notices of the Royal Astronomical Society, 181, pp. 375-389, 1977.
[3]	J.W. Swegle, D.A. Hicks, S.W. Attaway, Smooth particle hydrodynamics stability analysis, J. Comput. Phys. 116, pp. 123–134, 1995.
[4]	T. Belytschko, Y. Guo, W.K. Liu, S.P.Xiao, A unified stability analysis of meshless particle methods, Int. J. Numer. Methods Eng. 48, pp. 1359–1400 , 2000.
[5]	W.K. Liu, S. Jun, Y.F. Zhang, Reproducing kernel particle methods, Int. J. Numer. Methods Eng. 20 (8–9), pp. 1081–1106, 1995.
[6]	P.W. Randles, L.D. Libersky, Smoothed particle hydrodynamics: some recent improvements and applications, Comput. Methods Appl. Mech. Eng. 139, pp. 375–408, 1996.
[7]	G.R. Johnson, S.R. Beissel, Normalized smoothing functions for SPH impact computations, Int. J. Numer. Methods Engrg. 39, pp. 2725–2741, 1996.
[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.
[10]	M. Mabssout, M. Pastor, M.I. Herreros, M. Quecedo, A Runge–Kutta, Taylor–Galerkin scheme for hyperbolic systems with source terms. Application to shock wave propagation in viscoplastic geomaterials, Int. J. Numer. Anal. Methods Geomech. 30 (13), pp.1337–1355, 2006.
[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.
[12]	M. Mabssout, M. I. Herreros, Taylor-SPH vs Taylor-Galerkin for shock waves in viscoplastic continua, Eur. J. Comput. Mech. 20 (5-6), pp. 281-308, 2011.
[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.
[14]	P. Perzyna, Fundamental problems in viscoplasticity, Recent Advances in Applied Mechanics. Academic press, New York, 9, pp. 243-377 ,1966.
[15]	L. M. Kachanov, Introduction to Continuum Damage Mechanics, Martinus Nijhoff, Dordrecht, the Netherlands, 1986.
[16]	D. Krajcinovic, J. Lemaitre, Continuum Damage Mechanics, Theory and applications. Springer.Vienna. 1987.
[17]	T. Rabczuk, T. Belytschko, S. P. Xiao, Stable particle methods based on Lagrangian kernels, Comput. Methods. Appl. Mech. Engrg, 193, pp. 1035–1063, 2004.
[18]	J.J. Monaghan, J.C. Lattanzio, A refined particle method for astrophysical problems, Astronomy and Astrophysics, 149 , pp. 135 -143, 1985.

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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://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

Hajar Idder

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

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

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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

Copy | Download

@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}
}

Copy | Download

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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