International Journal of Fracture

, Volume 172, Issue 1, pp 41–52 | Cite as

A novel singular finite element on mixed-mode bimaterial interfacial cracks with arbitrary crack surface tractions

Original Paper


This paper investigates interfacial cracks with arbitrary crack surface tractions. A novel singular finite element which is constructed with the analytical solution around interfacial cracks is presented. Interfacial crack problems can be analyzed numerically using the singular finite element, and Mode I and/or Mode II stress intensity factors can be obtained directly. Unlike other enriched elements for cracks, neither extra unknowns nor transition elements are required. Numerical examples are given to illustrate the validity of present method.


Singular finite element Mixed-mode crack Symplectic dual approach Interfacial crack 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. ANSYS Release 11.0: (2007) Documentation for ANSYS. ANSYS Inc., PAGoogle Scholar
  2. Barsoum RP (1984) Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements. Int J Numer Methods Eng 11: 185–198Google Scholar
  3. Benzley SE (1974) Representation of singularities with isoparametric finite elements. Int J Numer Methods Eng 8: 537–545CrossRefGoogle Scholar
  4. Belytschko T, Lu YY, G L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37: 229–256CrossRefGoogle Scholar
  5. Dugdale DS (1960) Yielding of steel sheet containing slits. J Mech Phys Solids 8: 100–108CrossRefGoogle Scholar
  6. Fleming M, Chu YA, Moran B, Belytschko T (1997) Enriched element-free Galerkin methods for crack tip fields. Int J Numer Methods Eng 40: 1438–1504CrossRefGoogle Scholar
  7. Franca LP, Ramalho JVA, Valentin F (2006) Enriched finite element methods for unsteady reaction–diffusion problems. Commun Numer Methods Eng 22: 619–625CrossRefGoogle Scholar
  8. Fries TP, Belytschko T (2010) The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Methods Eng 84: 253–304Google Scholar
  9. Hatamleh O, Forman R, Shivakumar V, Lyons J (2005) Strip yield model numerical application to different geometries and loading conditions. Int J Fract 134: 251–265CrossRefGoogle Scholar
  10. Henshell RD, Shaw KG (1978) Crack tip finite elements are unnecessary. Int J Numer Methods Eng 9: 495–507CrossRefGoogle Scholar
  11. Hu XF, Yao WA, Fang ZX (2011) Stress singularity analysis of anisotropic multi-material wedges under antiplane shear deformation using the symplectic approach. Theor Appl Mech Lett 1: 061003CrossRefGoogle Scholar
  12. Ikeda T, Nagai M, Yamanaga K, Miyazaki N (2006) Stress intensity factor analyses of interface cracks between dissimilar anisotropic materials using the finite element method. Eng Fract Mech 73: 2067–2079CrossRefGoogle Scholar
  13. Li J, Zhang XB, Recho N (2001) Stress singularity near the tip of a two-dimensional formed from several elastic anisotropic materials. Int J Fract 107: 379–395CrossRefGoogle Scholar
  14. Liu GR, Gu YT (2001) A local radial point interpolation method (LR-PIM) for free vibration analysis of 2-D solids. J Sounds Vib 246: 29–46CrossRefGoogle Scholar
  15. Liew KM, Cheng Y, Kitipornchai S (2007) Analyzing the 2D fracture problems via the enriched boundary element-free method. Int J Solids Struct 44: 4220–4233CrossRefGoogle Scholar
  16. Lim CW, Cui S, Yao WA (2007) On new symplectic elasticity approach for exact bending solutions of rectangular thin plates with two opposite sides simply supported. Solids Struct 44: 5396–5411CrossRefGoogle Scholar
  17. Lim CW, Yao WA, Cui S (2008) Benchmark symplectic solutions for bending of corner-supported rectangular thin plates. IES J Part A Civ Struct Eng 1: 106–115CrossRefGoogle Scholar
  18. Lim CW, Xu XS (2010) Symplectic elasticity: theory and applications. Appl Mech Rev 63(050802): 1–10Google Scholar
  19. Miyazaki N, Ikeda T, Soda T, Munakata T (1993) Stress intensity factor analysis of interface crack using boundary elemental method-application of contour-integral method. Eng Fract Mech 45: 599–610CrossRefGoogle Scholar
  20. Moes N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69: 813–833CrossRefGoogle Scholar
  21. Murakami Y (1987) Stress intensity factors handbook. Pergamon Press, New YorkGoogle Scholar
  22. Nguyen V, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79: 763–813CrossRefGoogle Scholar
  23. Rice JR, Sih GC (1965) Plane problems of cracks in dissimilar media. J Appl Mech 32: 418–423CrossRefGoogle Scholar
  24. Williams ML (1959) The stress around a fault or crack in dissimilar media. Bull Seismol Soc Am 49: 199–208Google Scholar
  25. Yao WA, Zhong WX, Lim CW (2009) Symplectic elasticity. World Scientific, SingaporeCrossRefGoogle Scholar
  26. Zhang HW, Zhong WX (2003) Hamiltonian principle based stress singularity analysis near crack corners of multi-material junctions. Int J Solid Struct 40: 493–510CrossRefGoogle Scholar
  27. Zhong WX (1995) A new systematic methodology for theory of elasticity. Dalian University of Technology Press, Dalian (in Chinese)Google Scholar
  28. Zhou ZH, Xu XS, Leung AYT (2009) The mode III stress/electric intensity factors and singularities analysis for edge-cracked circular piezoelectric shafts. Int J Solids Struct 46: 3577–3586CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianPeople’s Republic of China

Personalised recommendations