Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 658160, 12 pages
http://dx.doi.org/10.1155/2013/658160
Research Article

Fracture Analysis of Brittle Materials Based on Nonlinear FEM and Application in Arch Dam with Fractures

1State Key Laboratory of Hydroscience and Hydraulic Engineering, Tsinghua University, Beijing 100084, China
2State Grid Xin Yuan Construction Co., Ltd., Beijing 100761, China
3China University of Mining & Technology, Beijing 100083, China

Received 7 June 2013; Revised 2 September 2013; Accepted 4 September 2013

Academic Editor: Pengcheng Fu

Copyright © 2013 Yuanwei Pan 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. A. Hillerborg, M. Modéer, and P. E. Petersson, “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements,” Cement and Concrete Research, vol. 6, no. 6, pp. 773–781, 1976. View at Google Scholar · View at Scopus
  2. Z. P. Bazant and B. H. Oh, “Crack band theory for fracture of concrete,” Meterials and Structures, vol. 16, no. 3, pp. 155–177, 1983. View at Google Scholar
  3. K. J. Willam and E. P. Warnke, “Constitutive models for the triaxial behavior of concrete,” in Proceedings of the International Association for Bridge and Structural Engineering, vol. 19, p. 174, ISMES, Bergamo, Italy, 1975.
  4. J. Kemeny and N. G. W. Cook, “Effective moduli, non-linear deformation and strength of a cracked elastic solid,” International Journal of Rock Mechanics and Mining Sciences and, vol. 23, no. 2, pp. 107–118, 1986. View at Google Scholar · View at Scopus
  5. G. R. Irwin, “Fracture dynamics,” in Fracturing of Metals, pp. 147–166, 1948. View at Google Scholar
  6. E. Orowan, “Fracture and strength of solids,” Reports on Progress in Physics, vol. 12, no. 1, pp. 185–232, 1948. View at Google Scholar
  7. J. R. Rice, “A path independent integral and the approximate analysis of strain concentration by notches and cracks,” Journal of Applied Mechanics, vol. 35, pp. 379–386, 1968. View at Publisher · View at Google Scholar
  8. G. C. Sih and B. Macdonald, “Fracture mechanics applied to engineering problems-strain energy density fracture criterion,” Engineering Fracture Mechanics, vol. 6, no. 2, pp. 361–386, 1974. View at Google Scholar · View at Scopus
  9. W. Yang, Macro-Micro Fracture Mechanics, National Industry Press, Beijing, China, 1995 (Chinese).
  10. M. G. D. Geers, R. De Borst, and R. H. J. Peerlings, “Damage and crack modeling in single-edge and double-edge notched concrete beams,” Engineering Fracture Mechanics, vol. 65, no. 2-3, pp. 247–261, 2000. View at Google Scholar · View at Scopus
  11. W. S. Blackburn, “Remeshing algorithm for three-dimensional crack growth and intersection with surfaces or cracks in non-coplanar planes,” Engineering Analysis with Boundary Elements, vol. 24, no. 4, pp. 343–350, 2000. View at Publisher · View at Google Scholar · View at Scopus
  12. J. C. W. van Vroonhoven and R. de Borst, “Combination of fracture and damage mechanics for numerical failure analysis,” International Journal of Solids and Structures, vol. 36, no. 8, pp. 1169–1191, 1998. View at Google Scholar · View at Scopus
  13. Z. P. Bazant, “Crack band model for fracture of geomaterials,” in Proceedings of the 4th International Conference on Numerical Methods in Geomechanics, vol. 3, pp. 1137–1152, Alberta, Canada, 1982.
  14. P. O. Bouchard, F. Bay, Y. Chastel, and I. Tovena, “Crack propagation modelling using an advanced remeshing technique,” Computer Methods in Applied Mechanics and Engineering, vol. 189, no. 3, pp. 723–742, 2000. View at Publisher · View at Google Scholar · View at Scopus
  15. N. Moës and E. Béchet, “Modeling stationary and evolving discontinuities with finite elements,” in Proceedings of the 7th International Conference on Computational Plasticity (COMPLAS '03), CIMNE, Barcelona, Spain, 2003.
  16. T. Belytschko, Y. Y. Lu, and L. Gu, “Element-free Galerkin methods,” International Journal for Numerical Methods in Engineering, vol. 37, no. 2, pp. 229–256, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. M. F. Marji, H. Hosseini-Nasab, and A. H. Kohsary, “On the uses of special crack tip elements in numerical rock fracture mechanics,” International Journal of Solids and Structures, vol. 43, no. 6, pp. 1669–1692, 2006. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Baghbanan and L. Jing, “Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture,” International Journal of Rock Mechanics and Mining Sciences, vol. 45, no. 8, pp. 1320–1334, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. G. H. Shi, “Manifold method,” in Proceedings of the 1st International Forum on DDA and Simulations of Discontinuous Media, Bekerley, Calif, USA, 1996.
  20. Y. H. Hatzor, A. A. Arzi, Y. Zaslavsky, and A. Shapira, “Dynamic stability analysis of jointed rock slopes using the DDA method: king Herod's Palace, Masada, Israel,” International Journal of Rock Mechanics and Mining Sciences, vol. 41, no. 5, pp. 813–832, 2004. View at Publisher · View at Google Scholar · View at Scopus
  21. H. Hakami, “Rock characterisation facility (RCF) shaft sinking—numerical computations using FLAC,” International Journal of Rock Mechanics and Mining Sciences, vol. 38, no. 1, pp. 59–65, 2001. View at Publisher · View at Google Scholar · View at Scopus
  22. Q. Yang, Y. Liu, Y. Chen, and W. Zhou, “Deformation reinforcement theory and its application to high arch dams,” Science in China E, vol. 51, no. 2, pp. 32–47, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. R. Hill, The Mathematical Theory of Plasticity, Clarendon Press, Oxford, UK, 1950. View at MathSciNet
  24. J. C. Simo, J. G. Kennedy, and S. Govindjee, “Nonsmooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms,” International Journal for Numerical Methods in Engineering, vol. 26, no. 10, pp. 2161–2185, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  25. O. C. Zienkiewicz and I. C. Cormeau, “Viscoplasticity-plasticity and creep in elastic solids-a unified numerical solution approach,” International Journal for Numerical Methods in Engineering, vol. 8, no. 4, pp. 821–845, 1974. View at Google Scholar · View at Scopus
  26. P. Perzyna, “Fundamental problems in viscoplasticity,” Advances in Applied Mechanics, vol. 9, no. 2, pp. 243–377, 1966. View at Publisher · View at Google Scholar · View at Scopus
  27. L. M. Kachanov, “Time of the rupture process under creep conditions,” Izvestiya Akademii Nauk SSR Otdelenie Tekhnicheskikh Nauk, vol. 8, pp. 26–31, 1958. View at Google Scholar
  28. I. N. Rabotnov, Creep Problems in Structural Members, vol. 7, North-Holland, Amsterdam, the Netherlands, 1969.
  29. U. Cicekli, G. Z. Voyiadjis, and R. K. Abu Al-Rub, “A plasticity and anisotropic damage model for plain concrete,” International Journal of Plasticity, vol. 23, no. 10-11, pp. 1874–1900, 2007. View at Publisher · View at Google Scholar · View at Scopus
  30. R. K. Abu Al-Rub and G. Z. Voyiadjis, “Gradient-enhanced coupled plasticity-anisotropic damage model for concrete fracture: computational aspects and applications,” International Journal of Damage Mechanics, vol. 18, no. 2, pp. 115–154, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. M. K. Darabi, R. K. Abu Al-Rub, E. A. Masad, C. W. Huang, and D. N. Little, “A thermo-viscoelastic-viscoplastic-viscodamage constitutive model for asphaltic materials,” International Journal of Solids and Structures, vol. 48, no. 1, pp. 191–207, 2011. View at Publisher · View at Google Scholar · View at Scopus