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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 293861, 12 pages
http://dx.doi.org/10.1155/2013/293861
Research Article

Explicit Dynamic Finite Element Method for Failure with Smooth Fracture Energy Dissipations

1Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 29208, USA
2STUCKY Ltd., Rue du Lac 33, 1020 Renens VD 1, Switzerland
3Department of Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA

Received 19 July 2013; Accepted 1 October 2013

Academic Editor: Timon Rabczuk

Copyright © 2013 Jeong-Hoon Song 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. T. Belytschko and T. Black, “Elastic crack growth in finite elements with minimal remeshing,” International Journal for Numerical Methods in Engineering, vol. 45, no. 5, pp. 601–620, 1999. View at Google Scholar · View at Scopus
  2. N. Moës, J. Dolbow, and T. Belytschko, “A finite element method for crack growth without remeshing,” International Journal for Numerical Methods in Engineering, vol. 46, no. 1, pp. 131–150, 1999. View at Google Scholar · View at Scopus
  3. C. Daux, N. Moës, J. Dolbow, N. Sukumar, and T. Belytschko, “Arbitrary branched and intersecting cracks with the extended finite element method,” International Journal for Numerical Methods in Engineering, vol. 48, no. 12, pp. 1741–1760, 2000. View at Google Scholar · View at Scopus
  4. P. M. A. Areias and T. Belytschko, “Analysis of three-dimensional crack initiation and propagation using the extended finite element method,” International Journal for Numerical Methods in Engineering, vol. 63, no. 5, pp. 760–788, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. Q. Duan, J. H. Song, T. Menouillard, and T. Belytschko, “Element-local level set method for three-dimensional dynamic crack growth,” International Journal for Numerical Methods in Engineering, vol. 80, no. 12, pp. 1520–1543, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. G. Zi and T. Belytschko, “New crack-tip elements for XFEM and applications to cohesive cracks,” International Journal for Numerical Methods in Engineering, vol. 57, no. 15, pp. 2221–2240, 2003. View at Publisher · View at Google Scholar · View at Scopus
  7. P. M. A. Areias, J. H. Song, and T. Belytschko, “Analysis of fracture in thin shells by overlapping paired elements,” Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 41–43, pp. 5343–5360, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. T. Belytschko, H. Chen, J. Xu, and G. Zi, “Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment,” International Journal for Numerical Methods in Engineering, vol. 58, no. 12, pp. 1873–1905, 2003. View at Publisher · View at Google Scholar · View at Scopus
  9. X.P. Xu and A. Needleman, “Numerical simulations of fast crack growth in brittle solids,” Journal of the Mechanics and Physics of Solids, vol. 42, no. 9, pp. 1397–1434, 1994. View at Google Scholar · View at Scopus
  10. M. Ortiz and A. Pandolfi, “Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis,” International Journal for Numerical Methods in Engineering, vol. 44, no. 9, pp. 1267–1282, 1999. View at Google Scholar · View at Scopus
  11. E. A. Repetto, R. Radovitzky, and M. Ortiz, “Finite element simulation of dynamic fracture and fragmentation of glass rods,” Computer Methods in Applied Mechanics and Engineering, vol. 183, no. 1-2, pp. 3–14, 2000. View at Google Scholar · View at Scopus
  12. F. Cirak, M. Ortiz, and A. Pandolfi, “A cohesive approach to thin-shell fracture and fragmentation,” Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 21-24, pp. 2604–2618, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. J.-H. Song, H. Wang, and T. Belytschko, “A comparative study on finite element methods for dynamic fracture,” Computational Mechanics, vol. 42, no. 2, pp. 239–250, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. J. H. Song, P. M. A. Areias, and T. Belytschko, “A method for dynamic crack and shear band propagation with phantom nodes,” International Journal for Numerical Methods in Engineering, vol. 67, no. 6, pp. 868–893, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. T. Menouillard and T. Belytschko, “Correction Force for releasing crack tip element with XFEM and only discontinuous enrichment,” European Journal of Computational Mechanics, vol. 18, no. 5-6, pp. 465–483, 2009. View at Google Scholar
  16. T. Menouillard, J. Réthoré, A. Combescure, and H. Bung, “Efficient explicit time stepping for the extended finite element method (X-FEM),” International Journal for Numerical Methods in Engineering, vol. 68, no. 9, pp. 911–939, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. T. Menouillard, J. Réthoré, N. Moës, A. Combescure, and H. Bung, “Mass lumping strategies for X-FEM explicit dynamics: application to crack propagation,” International Journal for Numerical Methods in Engineering, vol. 74, no. 3, pp. 447–474, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Hansbo and P. Hansbo, “A finite element method for the simulation of strong and weak discontinuities in solid mechanics,” Computer Methods in Applied Mechanics and Engineering, vol. 193, no. 35, pp. 3523–3540, 2004. View at Publisher · View at Google Scholar · View at Scopus
  19. J. H. Song and T. Belytschko, “Dynamic fracture of shells subjected to impulsive loads,” Journal of Applied Mechanics, Transactions of ASME, vol. 76, Article ID 051301, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. G. Ventura, J. X. Xu, and T. Belytschko, “A vector level set method and new discontinuity approximations for crack growth by EFG,” International Journal for Numerical Methods in Engineering, vol. 54, no. 6, pp. 923–944, 2002. View at Publisher · View at Google Scholar · View at Scopus
  21. G. Ventura, E. Budyn, and T. Belytschko, “Vector level sets for description of propagating cracks in finite elements,” International Journal for Numerical Methods in Engineering, vol. 58, no. 10, pp. 1571–1592, 2003. View at Publisher · View at Google Scholar · View at Scopus
  22. K. Ravi-Chandar, Dynamic Fracture, Elsevier Science, New York, NY, USA, 2004.
  23. L. B. Freund, Dynamic Fracture Mechanics, Cambridge University Press, Cambridge,UK, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  24. K. P. Galanis, Fracture of aluminum naval structures [Ph.D. thesis], Massachusetts Institute of Technology, 2007.
  25. K. P. Galanis and V. J. Papazoglou, “Effect of stiffening configurations on fracture of aluminium structures,” Strain, vol. 45, no. 2, pp. 131–138, 2009. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Ramulu and A. S. Kobayashi, “Mechanics of crack curving and branching—a dynamic fracture analysis,” International Journal of Fracture, vol. 27, no. 3-4, pp. 187–201, 1985. View at Publisher · View at Google Scholar · View at Scopus
  27. E. Sharon, S. P. Gross, and J. Fineberg, “Local crack branching as a mechanism for instability in dynamic fracture,” Physical Review Letters, vol. 74, no. 25, pp. 5096–5099, 1995. View at Google Scholar · View at Scopus
  28. E. Sharon and J. Fineberg, “Microbranching instability and the dynamic fracture of brittle materials,” Physical Review B, vol. 54, no. 10, pp. 7128–7139, 1996. View at Google Scholar · View at Scopus
  29. K. Ravi-Chandar, “Dynamic fracture of nominally brittle materials,” International Journal of Fracture, vol. 90, no. 1-2, pp. 83–102, 1998. View at Google Scholar · View at Scopus
  30. J. Fineberg, E. Sharon, and G. Cohen, “Crack front waves in dynamic fracture,” International Journal of Fracture, vol. 119, no. 3, pp. 247–261, 2003. View at Publisher · View at Google Scholar · View at Scopus
  31. T. Rabczuk and T. Belytschko, “Cracking particles: a simplified meshfree method for arbitrary evolving cracks,” International Journal for Numerical Methods in Engineering, vol. 61, no. 13, pp. 2316–2343, 2004. View at Publisher · View at Google Scholar · View at Scopus
  32. J. Lemaitre and J. L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, Cambridge, UK, 1990.
  33. N. Nguyen-Thanh, T. Rabczuk, H. Nguyen-Xuan, and S. P. A. Bordas, “A smoothed finite element method for shell analysis,” Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 2, pp. 165–177, 2008. View at Publisher · View at Google Scholar · View at Scopus
  34. P. Areias and T. Rabczuk, “Finite strain fracture of plates and shells with configurational forces and edge rotation,” International Journal For Numerical Methods in Engineering, vol. 94, no. 12, pp. 1099–1122, 2013. View at Publisher · View at Google Scholar