Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 371083, 10 pages
http://dx.doi.org/10.1155/2015/371083
Research Article

Cell-Based Smoothed Finite Element Method-Virtual Crack Closure Technique for a Piezoelectric Material of Crack

School of Mechanical Science and Engineering, Jilin University, Changchun 130025, China

Received 17 December 2014; Revised 5 February 2015; Accepted 5 February 2015

Academic Editor: Timon Rabczuk

Copyright © 2015 Li Ming Zhou 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. Y. E. Pak, “Crack extension force in a piezoelectric material,” Journal of Applied Mechanics, Transactions ASME, vol. 57, no. 3, pp. 647–653, 1990. View at Publisher · View at Google Scholar · View at Scopus
  2. H. Sosa, “Plane problems in piezoelectric media with defects,” International Journal of Solids and Structures, vol. 28, no. 4, pp. 491–505, 1991. View at Publisher · View at Google Scholar · View at Scopus
  3. Z. Suo, C.-M. Kuo, D. M. Barnett, and J. R. Willis, “Fracture mechanics for piezoelectric ceramics,” Journal of the Mechanics and Physics of Solids, vol. 40, no. 4, pp. 739–765, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. B. Wang, “Three-dimensional analysis of a flat elliptical crack in a piezoelectric material,” International Journal of Engineering Science, vol. 30, no. 6, pp. 781–791, 1992. View at Publisher · View at Google Scholar · View at Scopus
  5. T.-Y. Zhang and J. E. Hack, “Mode-III cracks in piezoelectric materials,” Journal of Applied Physics, vol. 71, no. 12, pp. 5865–5870, 1992. View at Publisher · View at Google Scholar · View at Scopus
  6. B. Aour, O. Rahmani, and M. Nait-Abdelaziz, “A coupled FEM/BEM approach and its accuracy for solving crack problems in fracture mechanics,” International Journal of Solids and Structures, vol. 44, no. 7-8, pp. 2523–2539, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. X. Guo, D. Fang, A. K. Soh, H. C. Kim, and J. J. Lee, “Analysis of piezoelectric ceramic multilayer actuators based on an electro-mechanical coupled meshless method,” Acta Mechanica Sinica, vol. 22, no. 1, pp. 34–39, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. C. Li, H. Man, C. Song, and W. Gao, “Fracture analysis of piezoelectric materials using the scaled boundary finite element method,” Engineering Fracture Mechanics, vol. 97, no. 1, pp. 52–71, 2012. View at Publisher · View at Google Scholar · View at Scopus
  9. E. Pan, “A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids,” Engineering Analysis with Boundary Elements, vol. 23, no. 1, pp. 67–76, 1999. View at Publisher · View at Google Scholar · View at Scopus
  10. H. Allik and T.J. R. Hughes, “Finite element method for piezoelectric vibration,” International Journal for Numerical Methods in Engineering, vol. 2, no. 2, pp. 151–157, 1970. View at Publisher · View at Google Scholar · View at Scopus
  11. G. R. Liu, T. T. Nguyen, K. Y. Dai, and K. Y. Lam, “Theoretical aspects of the smoothed finite element method (SFEM),” International Journal for Numerical Methods in Engineering, vol. 71, no. 8, pp. 902–930, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. O. C. Zienkiewicz, R. L. Taylor, and J. M. Too, “Reduced integration technique in general analysis of plates and shells,” International Journal for Numerical Methods in Engineering, no. 3, pp. 275–290, 1971. View at Google Scholar · View at Scopus
  13. G. R. Liu, K. Y. Dai, and T. T. Nguyen, “A smoothed finite element method for mechanics problems,” Computational Mechanics, vol. 39, no. 6, pp. 859–877, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. 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
  15. H. Nguyen-Xuan, G. R. Liu, T. Nguyen-Thoi, and C. Nguyen-Tran, “An edge-based smoothed finite element method for analysis of two-dimensional piezoelectric structures,” Smart Materials and Structures, vol. 18, no. 6, Article ID 065015, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. H. Nguyen-Xuan, G. Liu, S. Bordas, S. Natarajan, and T. SandRabczuk, “An adaptive singular es-fem for mechanics problems with singular field of arbitrary order,” Computer Methods in Applied Mechanics and Engineering, vol. 253, pp. 252–273, 2013. View at Google Scholar
  17. S. C. Wu, G. R. Liu, X. Y. Cui, T. T. Nguyen, and G. Y. Zhang, “An edge-based smoothed point interpolation method (ES-PIM) for heat transfer analysis of rapid manufacturing system,” International Journal of Heat and Mass Transfer, vol. 53, no. 9-10, pp. 1938–1950, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. Z. C. He, A. G. Cheng, G. Y. Zhang, Z. H. Zhong, and G. R. Liu, “Dispersion error reduction for acoustic problems using the edge-based smoothed finite element method (ES-FEM),” International Journal for Numerical Methods in Engineering, vol. 86, no. 11, pp. 1322–1338, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. T. Rabczuk, G. Zi, A. Gerstenberger, and W. A. Wall, “A new crack tip element for the phantom-node method with arbitrary cohesive cracks,” International Journal for Numerical Methods in Engineering, vol. 75, no. 5, pp. 577–599, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. Z. Wu, L. N. Y. Wong, and L. Fan, “Dynamic study on fracture problems in viscoelastic sedimentary rocks using the numerical manifold method,” Rock Mechanics and Rock Engineering, vol. 46, no. 6, pp. 1415–1427, 2013. View at Publisher · View at Google Scholar · View at Scopus
  21. 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 MathSciNet · View at Scopus
  22. Y. Y. Lu, T. Belytschko, and L. Gu, “A new implementation of the element free Galerkin method,” Computer Methods in Applied Mechanics and Engineering, vol. 113, no. 3-4, pp. 397–414, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. 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
  24. J. Shi, W. Ma, and N. Li, “Extended meshless method based on partition of unity for solving multiple crack problems,” Meccanica, vol. 48, no. 9, pp. 2263–2270, 2013. View at Publisher · View at Google Scholar · View at Scopus
  25. S. S. Nanthakumar, T. Lahmer, and T. Rabczuk, “Detection of multiple flaws in piezoelectric structures using XFEM and level sets,” Computer Methods in Applied Mechanics and Engineering, vol. 275, pp. 98–112, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. E. Béchet, M. Scherzer, and M. Kuna, “Application of the X-FEM to the fracture of piezoelectric materials,” International Journal for Numerical Methods in Engineering, vol. 77, no. 11, pp. 1535–1565, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. H. Nguyen-Vinh, I. Bakar, M. A. Msekh et al., “Extended finite element method for dynamic fracture of piezo-electric materials,” Engineering Fracture Mechanics, vol. 92, pp. 19–31, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. E. F. Rybicki and M. F. Kanninen, “A finite element calculation of stress intensity factors by a modified crack closure integral,” Engineering Fracture Mechanics, vol. 9, no. 4, pp. 931–938, 1977. View at Publisher · View at Google Scholar · View at Scopus
  29. D. Xie and S. B. Biggers Jr., “Progressive crack growth analysis using interface element based on the virtual crack closure technique,” Finite Elements in Analysis and Design, vol. 42, no. 11, pp. 977–984, 2006. View at Publisher · View at Google Scholar · View at Scopus
  30. D. Xie and S. B. Biggers Jr., “Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part I: formulation and validation,” Engineering Fracture Mechanics, vol. 73, no. 6, pp. 771–785, 2006. View at Publisher · View at Google Scholar · View at Scopus
  31. R. Krueger, “Virtual crack closure technique: history, approach, and applications,” Applied Mechanics Reviews, vol. 57, no. 2, pp. 109–143, 2004. View at Publisher · View at Google Scholar · View at Scopus
  32. S. K. Maiti, “Finite element computation of crack closure integrals and stress intensity factors,” Engineering Fracture Mechanics, vol. 41, no. 3, pp. 339–348, 1992. View at Publisher · View at Google Scholar · View at Scopus
  33. P. A. Wawrzynek and A. R. Ingraffea, “An interactive approach to local remeshing around a propagating crack,” Finite Elements in Analysis and Design, vol. 5, no. 1, pp. 87–96, 1989. View at Publisher · View at Google Scholar · View at Scopus
  34. Y.-S. Chang, J.-B. Choi, Y.-J. Kim, and G. Yagawa, “Numerical calculation of energy release rates by virtual crack closure technique,” KSME International Journal, vol. 18, no. 11, pp. 1996–2008, 2004. View at Google Scholar · View at Scopus
  35. J.-H. Kim and G. H. Paulino, “Mixed-mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure method,” Engineering Fracture Mechanics, vol. 69, no. 14–16, pp. 1557–1586, 2002. View at Publisher · View at Google Scholar · View at Scopus
  36. D. Xie and S. B. Biggers Jr., “Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part II: sensitivity study on modeling details,” Engineering Fracture Mechanics, vol. 73, no. 6, pp. 786–801, 2006. View at Publisher · View at Google Scholar · View at Scopus