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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 808359, 14 pages
http://dx.doi.org/10.1155/2014/808359
Research Article

A Modified SPH Method for Dynamic Failure Simulation of Heterogeneous Material

1School of Civil, Environmental, and Ming Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
2Institute of Geotechnical and Underground Engineering, Beijing University of Technology, Beijing 100124, China
3School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798

Received 9 January 2014; Accepted 15 February 2014; Published 22 April 2014

Academic Editor: Yumin Cheng

Copyright © 2014 G. W. Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Tapponnier and W. F. Brace, “Development of stress-induced microcracks in Westerly Granite,” International Journal of Rock Mechanics and Mining Sciences and, vol. 13, no. 4, pp. 103–112, 1976. View at Google Scholar · View at Scopus
  2. T.-F. Wong, “Micromechanics of faulting in westerly granite,” International Journal of Rock Mechanics and Mining Sciences and, vol. 19, no. 2, pp. 49–64, 1982. View at Google Scholar · View at Scopus
  3. S. C. Blair and N. G. W. Cook, “Analysis of compressive fracture in rock using statistical techniques: part I. A non-linear rule-based model,” International Journal of Rock Mechanics and Mining Sciences, vol. 35, no. 7, pp. 837–848, 1998. View at Google Scholar · View at Scopus
  4. C. A. Tang, H. Liu, P. K. K. Lee, Y. Tsui, and L. G. Tham, “Numerical studies of the influence of microstructure on rock failure in uniaxial compression-part I: effect of heterogeneity,” International Journal of Rock Mechanics and Mining Sciences, vol. 37, no. 4, pp. 555–569, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. Z. Fang and J. P. Harrison, “Development of a local degradation approach to the modelling of brittle fracture in heterogeneous rocks,” International Journal of Rock Mechanics and Mining Sciences, vol. 39, no. 4, pp. 443–457, 2002. View at Publisher · View at Google Scholar · View at Scopus
  6. D. O. Potyondy and P. A. Cundall, “A bonded-particle model for rock,” International Journal of Rock Mechanics and Mining Sciences, vol. 41, no. 8, pp. 1329–1364, 2004. View at Publisher · View at Google Scholar · View at Scopus
  7. L. Lucy, “A numerical approach to the testing of the fission hypothesis (close binary star formation),” The Astronomical Journal, vol. 82, no. 12, pp. 1013–1024, 1977. View at Google Scholar
  8. R. A. Gingold and J. J. Monaghan, “Smoothed particle hydrodynamics: theory and application to non-spherical stars,” Monthly Notices of the Royal Astronomical Society, vol. 181, no. 2, pp. 375–389, 1977. View at Google Scholar
  9. L. D. Libersky and A. G. Petschek, “Smoothed particle hydrodynamics with strength of materials,” in Advances in the Free-Lagrange Method Including Contributions on Adaptive Gridding and the Smooth Particle, vol. 395 of Lecture Notes in Physics, pp. 248–257, 1990. View at Google Scholar
  10. J. J. Monaghan, “Smoothed particle hydrodynamics,” Annual Review of Astronomy and Astrophysics, vol. 30, no. 1, pp. 543–574, 1992. View at Google Scholar · View at Scopus
  11. L. D. Libersky, A. G. Petschek, T. C. Carney, J. R. Hipp, and F. A. Allahdadi, “High strain lagrangian hydrodynamics a three-dimensional SPH code for dynamic material response,” Journal of Computational Physics, vol. 109, no. 1, pp. 67–75, 1993. View at Publisher · View at Google Scholar · View at Scopus
  12. J. J. Monaghan, “Smoothed particle hydrodynamics,” Reports on Progress in Physics, vol. 68, no. 8, pp. 1703–1759, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. J. Monaghan and J. C. Lattanzio, “A refined particle method for astrophysical problems,” Astronomy & Astrophysics, vol. 149, no. 1, pp. 135–143, 1985. View at Google Scholar
  14. P. W. Randles and L. D. Libersky, “Smoothed particle hydrodynamics: some recent improvements and applications,” Computer Methods in Applied Mechanics and Engineering, vol. 139, no. 1–4, pp. 375–408, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. M. Shimrat, “Algorithm 112: position of point relative to polygon,” Communications of the ACM, vol. 5, no. 8, p. 434, 1962. View at Google Scholar
  16. B. Didier, An Efficient Ray-Polygon Intersection. Graphics Gems, Academic Press Professional, 1990.
  17. E. Haines, Point in Polygon Strategies., Academic Press, 1994.
  18. Geological Unit of Singapore, Geology of the Republic of Singapore, Public Works Department, Singapore, 1976.
  19. M.-H. Yu, Y.-W. Zan, J. Zhao, and M. Yoshimine, “A Unified Strength criterion for rock material,” International Journal of Rock Mechanics and Mining Sciences, vol. 39, no. 8, pp. 975–989, 2002. View at Publisher · View at Google Scholar · View at Scopus
  20. G. W. Ma, X. J. Wang, and Q. M. Li, “Modeling strain rate effect of heterogeneous materials using SPH method,” Rock Mechanics and Rock Engineering, vol. 43, no. 6, pp. 763–776, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. G. W. Ma, X. J. Wang, and F. Ren, “Numerical simulation of compressive failure of heterogeneous rock-like materials using SPH method,” International Journal of Rock Mechanics and Mining Sciences, vol. 48, no. 3, pp. 353–363, 2011. View at Publisher · View at Google Scholar · View at Scopus
  22. G. E. Andreev, Brittle Failure of Rock Materials: Test Results and Constitutive Models, A.A. Balkema, Rotterdam, The Netherlands, 1995.