Skip to main content
Log in

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

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • ANSYS Release 11.0: (2007) Documentation for ANSYS. ANSYS Inc., PA

    Google Scholar 

  • Barsoum RP (1984) Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements. Int J Numer Methods Eng 11: 185–198

    Google Scholar 

  • Benzley SE (1974) Representation of singularities with isoparametric finite elements. Int J Numer Methods Eng 8: 537–545

    Article  Google Scholar 

  • Belytschko T, Lu YY, G L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37: 229–256

    Article  Google Scholar 

  • Dugdale DS (1960) Yielding of steel sheet containing slits. J Mech Phys Solids 8: 100–108

    Article  Google Scholar 

  • Fleming M, Chu YA, Moran B, Belytschko T (1997) Enriched element-free Galerkin methods for crack tip fields. Int J Numer Methods Eng 40: 1438–1504

    Article  Google Scholar 

  • Franca LP, Ramalho JVA, Valentin F (2006) Enriched finite element methods for unsteady reaction–diffusion problems. Commun Numer Methods Eng 22: 619–625

    Article  Google Scholar 

  • 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: 253–304

    Google Scholar 

  • Hatamleh O, Forman R, Shivakumar V, Lyons J (2005) Strip yield model numerical application to different geometries and loading conditions. Int J Fract 134: 251–265

    Article  Google Scholar 

  • Henshell RD, Shaw KG (1978) Crack tip finite elements are unnecessary. Int J Numer Methods Eng 9: 495–507

    Article  Google Scholar 

  • 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: 061003

    Article  Google Scholar 

  • 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: 2067–2079

    Article  Google Scholar 

  • 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: 379–395

    Article  Google Scholar 

  • 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: 29–46

    Article  Google Scholar 

  • Liew KM, Cheng Y, Kitipornchai S (2007) Analyzing the 2D fracture problems via the enriched boundary element-free method. Int J Solids Struct 44: 4220–4233

    Article  Google Scholar 

  • 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: 5396–5411

    Article  Google Scholar 

  • 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: 106–115

    Article  Google Scholar 

  • Lim CW, Xu XS (2010) Symplectic elasticity: theory and applications. Appl Mech Rev 63(050802): 1–10

    Google Scholar 

  • 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: 599–610

    Article  Google Scholar 

  • Moes N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69: 813–833

    Article  Google Scholar 

  • Murakami Y (1987) Stress intensity factors handbook. Pergamon Press, New York

    Google Scholar 

  • Nguyen V, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79: 763–813

    Article  Google Scholar 

  • Rice JR, Sih GC (1965) Plane problems of cracks in dissimilar media. J Appl Mech 32: 418–423

    Article  Google Scholar 

  • Williams ML (1959) The stress around a fault or crack in dissimilar media. Bull Seismol Soc Am 49: 199–208

    Google Scholar 

  • Yao WA, Zhong WX, Lim CW (2009) Symplectic elasticity. World Scientific, Singapore

    Book  Google Scholar 

  • Zhang HW, Zhong WX (2003) Hamiltonian principle based stress singularity analysis near crack corners of multi-material junctions. Int J Solid Struct 40: 493–510

    Article  Google Scholar 

  • Zhong WX (1995) A new systematic methodology for theory of elasticity. Dalian University of Technology Press, Dalian (in Chinese)

    Google Scholar 

  • 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: 3577–3586

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to W. A. Yao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hu, X.F., Yao, W.A. A novel singular finite element on mixed-mode bimaterial interfacial cracks with arbitrary crack surface tractions. Int J Fract 172, 41–52 (2011). https://doi.org/10.1007/s10704-011-9645-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-011-9645-3

Keywords

Navigation