Table of Contents Author Guidelines Submit a Manuscript
Advances in Materials Science and Engineering
Volume 2016, Article ID 4125307, 14 pages
http://dx.doi.org/10.1155/2016/4125307
Research Article

A Cell-Based Smoothed XFEM for Fracture in Piezoelectric Materials

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

Received 29 July 2015; Revised 23 November 2015; Accepted 9 December 2015

Academic Editor: Bert Blocken

Copyright © 2016 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. M. Li, J. X. Yuan, D. Guan, and W. M. Chen, “Application of piezoelectric fiber composite actuator to aircraft wing for aerodynamic performance improvement,” Science China Technological Sciences, vol. 54, no. 2, pp. 395–402, 2011. View at Publisher · View at Google Scholar · View at Scopus
  2. M. Kuna, “Finite element analyses of crack problems in piezoelectric structures,” Computational Materials Science, vol. 13, no. 1–3, pp. 67–80, 1998. View at Publisher · View at Google Scholar · View at Scopus
  3. J. Meckerle, “Smart materials and structures—a finite element approach—an addendum: a bibliography (1997–2002),” Modelling and Simulation in Materials Science and Engineering, vol. 11, no. 5, pp. 707–744, 2003. View at Google Scholar
  4. F. García-Sánchez, Ch. Zhang, and A. Sáez, “2-D transient dynamic analysis of cracked piezoelectric solids by a time-domain BEM,” Computer Methods in Applied Mechanics and Engineering, vol. 197, no. 33-40, pp. 3108–3121, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. Ch. Zhang, F. García-Sánchez, and A. Sáez, “Time-domain BEM analysis of cracked piezoelectric solids under impact loading,” in Computational Mechanics: Proceedings of “International Symposium on Computational Mechanics” July 30–August 1, 2007, Beijing, China, pp. 206–218, Springer, Berlin, Germany, 2009. View at Publisher · View at Google Scholar
  6. J. Sladek, V. Sladek, C. Zhang, P. Solek, and L. Starek, “Fracture analyses in continuously nonhomogeneous piezoelectric solids by the MLPG,” Computer Modeling in Engineering and Sciences, vol. 19, no. 3, pp. 247–262, 2007. View at Google Scholar · View at MathSciNet
  7. S. Nanthakumar, T. Lahmer, X. Zhuang, G. Zi, and T. Rabczuk, “Detection of material interfaces using a regularized level set method in piezoelectric structures,” Inverse Problems in Science and Engineering, pp. 1–24, 2015. View at Publisher · View at Google Scholar
  8. S. S. Nanthakumar, T. Lahmer, and T. Rabczuk, “Detection of flaws in piezoelectric structures using extended FEM,” International Journal for Numerical Methods in Engineering, vol. 96, no. 6, pp. 373–389, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. 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
  10. 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 Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. Y. E. Pak, “Linear electro-elastic fracture mechanics of piezoelectric materials,” International Journal of Fracture, vol. 54, no. 1, pp. 79–100, 1992. View at Publisher · View at Google Scholar · View at Scopus
  12. X.-L. Xu and R. K. N. D. Rajapakse, “Analytical solution for an arbitrarily oriented void/crack and fracture of piezoceramics,” Acta Materialia, vol. 47, no. 6, pp. 1735–1747, 1999. View at Publisher · View at Google Scholar · View at Scopus
  13. 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 Zentralblatt MATH · View at Scopus
  14. M. Kuna, “Fracture mechanics of piezoelectric materials—where are we right now?” Engineering Fracture Mechanics, vol. 77, no. 2, pp. 309–326, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Kuna, “Finite element analyses of cracks in piezoelectric structures: a survey,” Archive of Applied Mechanics, vol. 76, no. 11-12, pp. 725–745, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. R. R. Bhargava and K. Sharma, “X-FEM studies on an inclined crack in a 2-D finite piezoelectric media,” in Future Communication, Computing, Control and Management, vol. 141 of Lecture Notes in Electrical Engineering, pp. 285–290, Springer, Berlin, Germany, 2012. View at Publisher · View at Google Scholar
  17. M. Abendroth, U. Groh, M. Kuna, and A. Ricoeur, “Finite element-computation of the electromechanical J-integral for 2-D and 3-D crack analysis,” International Journal of Fracture, vol. 114, no. 4, pp. 359–378, 2002. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. Motola and L. Banks-Sills, “M-integral for calculating intensity factors of cracked piezoelectric materials using the exact boundary conditions,” Journal of Applied Mechanics, vol. 76, no. 1, Article ID 011004, 9 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. R. R. Bhargava and K. Sharma, “A study of finite size effects on cracked 2-D piezoelectric media using extended finite element method,” Computational Materials Science, vol. 50, no. 6, pp. 1834–1845, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. 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
  21. 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
  22. T. Nguyen-Thoi, T. Bui-Xuan, P. Phung-Van, H. Nguyen-Xuan, and P. Ngo-Thanh, “Static, free vibration and buckling analyses of stiffened plates by CS-FEM-DSG3 using triangular elements,” Computers & Structures, vol. 125, pp. 100–113, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. C. V. Le, H. Nguyen-Xuan, H. Askes et al., “A cellbased smoothed finite element method for kinematic limit analysis,” International Journal for Numerical Methods in Engineering, vol. 83, no. 12, pp. 1651–1674, 2010. View at Google Scholar
  24. G. R. Liu, T. Nguyen-Thoi, and K. Y. Lam, “An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids,” Journal of Sound and Vibration, vol. 320, no. 4-5, pp. 1100–1130, 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. N. Nguyen-Thanh, T. Rabczuk, H. Nguyen-Xuan, and S. P. A. Bordas, “An alternative alpha finite element method (AαFEM) for free and forced structural vibration using triangular meshes,” Journal of Computational and Applied Mathematics, vol. 233, no. 9, pp. 2112–2135, 2010. View at Publisher · View at Google Scholar
  26. T. Nguyen-Thoi, G. R. Liu, K. Y. Lam, and G. Y. Zhang, “A face-based smoothed finite element method (FS-FEM) for 3D linear and geometrically non-linear solid mechanics problems using 4-node tetrahedral elements,” International Journal for Numerical Methods in Engineering, vol. 78, no. 3, pp. 324–353, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. H. Nguyen-Xuan, T. Rabczuk, N. Nguyen-Thanh, T. Nguyen-Thoi, and S. Bordas, “A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates,” Computational Mechanics, vol. 46, no. 5, pp. 679–701, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  28. H. Nguyen-Xuan, L. V. Tran, T. Nguyen-Thoi, and H. C. Vu-Do, “Analysis of functionally graded plates using an edge-based smoothed finite element method,” Composite Structures, vol. 93, no. 11, pp. 3019–3039, 2011. View at Publisher · View at Google Scholar · View at Scopus
  29. G. R. Liu, H. Nguyen-Xuan, T. Nguyen-Thoi, and X. Xu, “A novel Galerkin-like weakform and a superconvergent alpha finite element method (SαFEM) for mechanics problems using triangular meshes,” Journal of Computational Physics, vol. 228, no. 11, pp. 4055–4087, 2009. View at Publisher · View at Google Scholar · View at Scopus
  30. H. Nguyen-Xuan, L. V. Tran, C. H. Thai, and T. Nguyen-Thoi, “Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing,” Thin-Walled Structures, vol. 54, pp. 1–18, 2012. View at Publisher · View at Google Scholar · View at Scopus
  31. H. Nguyen-Xuan, T. Rabczuk, T. Nguyen-Thoi, T. N. Tran, and N. Nguyen-Thanh, “Computation of limit and shakedown loads using a node-based smoothed finite element method,” International Journal for Numerical Methods in Engineering, vol. 90, no. 3, pp. 287–310, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  32. H. Nguyen-Xuan, G. R. Liu, N. Nourbakhshnia, and L. Chen, “A novel singular ES-FEM for crack growth simulation,” Engineering Fracture Mechanics, vol. 84, pp. 41–66, 2012. View at Publisher · View at Google Scholar · View at Scopus
  33. N. Nourbakhshnia and G. R. Liu, “A quasistatic crack growth simulation based on the singular ESFEM,” International Journal for Numerical Methods in Engineering, vol. 88, no. 5, pp. 473–492, 2011. View at Publisher · View at Google Scholar · View at Scopus
  34. W. Zeng, G. R. Liu, Y. Kitamura, and H. Nguyen-Xuan, “A three-dimensional ES-FEM for fracture mechanics problems in elastic solids,” Engineering Fracture Mechanics, vol. 114, pp. 127–150, 2013. View at Publisher · View at Google Scholar · View at Scopus
  35. P. Phung-Van, T. Nguyen-Thoi, T. Le-Dinh, and H. Nguyen-Xuan, “Static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators by the cell-based smoothed discrete shear gap method (CS-FEM-DSG3),” Smart Materials and Structures, vol. 22, no. 9, Article ID 095026, 2013. View at Publisher · View at Google Scholar · View at Scopus
  36. P. Phung-Van, L. De Lorenzis, C. H. Thai, M. Abdel-Wahab, and H. Nguyen-Xuan, “Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements,” Computational Materials Science, vol. 96, pp. 495–505, 2015. View at Publisher · View at Google Scholar · View at Scopus
  37. S. P. A. Bordas, T. Rabczuk, N.-X. Hung et al., “Strain smoothing in FEM and XFEM,” Computers & Structures, vol. 88, no. 23-24, pp. 1419–1443, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. X. Zhao, S. P. A. Bordas, and J. Qu, “A hybrid smoothed extended finite element/level set method for modeling equilibrium shapes of nano-inhomogeneities,” Computational Mechanics, vol. 52, no. 6, pp. 1417–1428, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. L. Chen, T. Rabczuk, S. P. A. Bordas, G. R. Liu, K. Y. Zeng, and P. Kerfriden, “Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth,” Computer Methods in Applied Mechanics and Engineering, vol. 209–212, pp. 250–265, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. Y. Jiang, T. E. Tay, L. Chen, and X. S. Sun, “An edge-based smoothed XFEM for fracture in composite materials,” International Journal of Fracture, vol. 179, no. 1-2, pp. 179–199, 2013. View at Publisher · View at Google Scholar · View at Scopus
  41. N. Vu-Bac, H. Nguyen-Xuan, L. Chen et al., “A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis,” Computer Modeling in Engineering and Sciences, vol. 73, no. 4, pp. 331–355, 2011. View at Google Scholar · View at MathSciNet
  42. E. Bechet, 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, pp. 1535–1599, 2009. View at Google Scholar
  43. U. Groh and M. Kuna, “Efficient boundary element analysis of cracks in 2D piezoelectric structures,” International Journal of Solids and Structures, vol. 42, no. 8, pp. 2399–2416, 2005. View at Publisher · View at Google Scholar · View at Scopus
  44. L. M. Zhou, G. W. Meng, F. Li, and H. Wang, “Cell-based smoothed finite element method-virtual crack closure technique for a piezoelectric material of crack,” Mathematical Problems in Engineering, vol. 2015, Article ID 371083, 10 pages, 2015. View at Publisher · View at Google Scholar
  45. P. Laborde, J. Pommier, Y. Renard, and M. Salaün, “High-order extended finite element method for cracked domains,” International Journal for Numerical Methods in Engineering, vol. 64, no. 3, pp. 354–381, 2005. View at Publisher · View at Google Scholar · View at Scopus
  46. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  47. T. Rabczuk and T. Belytschko, “Cracking particles: a simplified mesh-free 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
  48. T. Rabczuk, G. Zi, S. Bordas, and H. Nguyen-Xuan, “A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures,” Engineering Fracture Mechanics, vol. 75, no. 16, pp. 4740–4758, 2008. View at Publisher · View at Google Scholar · View at Scopus
  49. J. R. Rice, “Mathematical analysis in the mechanics of fracture,” in Fracture: An Advanced Treatise, H. Liebowitz, Ed., vol. 2, pp. 191–311, Academic Press, New York, NY, USA, 1968. View at Google Scholar
  50. J. D. Eshelby, “Energy relations and the energy-momentum tensor in continuum mechanics,” in Inelastic Behavior of Solids, M. F. Kanninen, W. F. Adler, A. R. Rosenfield, and R. I. Jaffee, Eds., pp. 77–115, McGraw-Hill, New York, NY, USA, 1970. View at Google Scholar