Skip to main content
SpringerLink
Log in

A singular edge-based smoothed finite element method (ES-FEM) for bimaterial interface cracks

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

The recently developed edge-based smoothed finite element method (ES-FEM) is extended to the mix-mode interface cracks between two dissimilar isotropic materials. The present ES-FEM method uses triangular elements that can be generated automatically for problems even with complicated geometry, and strains are smoothed over the smoothing domains associated with the edges of elements. Considering the stress singularity in the vicinity of the bimaterial interface crack tip is of the inverse square root type together with oscillatory nature, a five-node singular crack tip element is devised within the framework of ES-FEM to construct singular shape functions. Such a singular element can be easily implemented since the derivatives of the singular shape term \({(1/\sqrt r)}\) are not needed. The mix-mode stress intensity factors can also be easily evaluated by an appropriate treatment during the domain form of the interaction integral. The effectiveness of the present singular ES-FEM is demonstrated via benchmark examples for a wide range of material combinations and boundary conditions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yeap KB, Zeng KY, Chi DZ (2008) Determining the interfacial toughness of low-k films on Si substrate by wedge indentation: further studies. Acta Mater 56: 977–984

    Article  Google Scholar 

  2. Hutchinson JW, Suo Z (1992) Mixed mode cracking in layered materials. In: Hutchinson JW, Wu TY (eds) Advances in applied mechanics, pp 63–191

  3. Williams ML (1959) The stress around a fault or crack in dissimilar media. Bullet Seismol Soc Am 49: 199–204

    Google Scholar 

  4. England AH (1965) A crack between dissimilar media. J Appl Mech 32: 400–402

    Google Scholar 

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

    Google Scholar 

  6. Rice JR (1988) Elastic fracture mechanics concepts for interfacial cracks. J Appl Mech 55: 98–103

    Article  Google Scholar 

  7. Henshell RD, Shaw KG (1975) Crack tip finite elements are unnecessary. Int J Numer Methods Eng 9: 495–507

    Article  MATH  Google Scholar 

  8. Barsoum RS (1976) On the use of isoparametric finite elements in linear fracture mechanics. Int J Numer Methods Eng 10: 551–564

    Article  MATH  Google Scholar 

  9. Barsoum RS (1977) Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements. Int J Numer Methods Eng 11: 85–98

    Article  MATH  Google Scholar 

  10. Shih CF, Asaro RJ (1988) Elastic-plastic analysis of cracks on bimaterial interfaces: part I-small scale yielding. J Appl Mech 55: 299–316

    Article  Google Scholar 

  11. Matos PPL, McMeeking RM, Charalambides PG, Drory MD (1989) A method for calculating stress intensities in bimaterial fracture. Int J Fract 40: 235–254

    Article  Google Scholar 

  12. Nahta R, Moran B (1993) Domain integrals for axisymmetric interface crack problems. Int J Solids Struct 30(15): 2027–2040

    Article  MATH  Google Scholar 

  13. Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5): 601–620

    Article  MATH  MathSciNet  Google Scholar 

  14. Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1): 131–150

    Article  MATH  Google Scholar 

  15. Belytschko T, Moes N, Usui S, Parimi C (2001) Arbitrary discontinuities in finite elements. Int J Numer Methods Eng 50(4): 993–1013

    Article  MATH  Google Scholar 

  16. Sukumar N, Huang ZY, Prévost JH, Suo Z (2004) Partition of unity enrichment for bimaterial interface cracks. Int J Numer Methods Eng 59: 1075–1102

    Article  MATH  Google Scholar 

  17. Chen JS, Wu CT, Yoon Y (2001) A stabilized conforming nodal integration for Galerkin mesh-free methods. Int J Numer Methods Eng 50: 435–466

    Article  MATH  Google Scholar 

  18. Liu GR, Dai KY, Nguyen TT (2007) A smoothed finite element method for mechanics problems. Comput Mech 39: 859–877

    Article  MATH  Google Scholar 

  19. Liu GR, Nguyen TT, Dai KY, Lam KY (2007) Theoretical aspects of the smoothed finite element method (SFEM). Int J Numer Methods Eng 71: 902–930

    Article  MathSciNet  Google Scholar 

  20. Liu GR, Nguyen-Thoi T, Lam KY (2008) A node-based smoothed finite element method for upper bound solution to solid problems (NS-FEM). Comput Struct 87: 14–26

    Article  Google Scholar 

  21. Dohrmann CR, Heinstein MW, Jung J, Key SW, Witkowski WR (2000) Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes. Int J Numer Methods Eng 47: 1549–1568

    Article  MATH  Google Scholar 

  22. Liu GR, Zhang GY, Dai KY, Wang YY, Zhong ZH, Li GY, Han X (2005) A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems. Int J Comput Methods 2(4): 645–665

    Article  MATH  Google Scholar 

  23. Liu GR, Nguyen-Thoi T, Lam KY (2009) An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analysis. J Sound Vib 320: 1100–1130

    Article  Google Scholar 

  24. Nguyen-Thoi T, Liu GR, Lam KY (2009) A face-based smoothed finite element method (FS-FEM) for 3D linear and nonlinear solid mechanics problems using 4-node tetrahedral elements. Int J Numer Methods Eng 78: 324–353

    Article  MathSciNet  Google Scholar 

  25. Liu GR, Gu YT (2001) A point interpolation method for two-dimensional solids. Int J Numer Methods Eng 50: 937–951

    Article  MATH  Google Scholar 

  26. Liu GR, Zhang GY (2008) Edge-based smoothed point interpolation methods. Int J Comput Methods 5: 621–646

    Article  MathSciNet  Google Scholar 

  27. Chen L, Nguyen-Xuan H, Nguyen-Thoi T, Zeng KY, Wu SC (2009) Assessment of smoothed point interpolation methods for elastic mechanics. Commu Numer Methods Eng doi:10.1002/cnm.1251

  28. Shih CF (1988) Cracks on bimaterial interfaces: elasticity and plasticity aspects. Mater Sci Eng A 143: 77–90

    Google Scholar 

  29. Dundurs J (1969) Edge-bonded dissimilar orthogonal elastic wedges. J Appl Mech 36: 650–652

    Google Scholar 

  30. Moran B, Shih CF (1987) Crack tip and associated domain integrals from momentum and energy balance. Eng Fract Mech 27(6): 615–641

    Article  Google Scholar 

  31. Li FZ, Shih CF, Needleman A (1985) A comparison of methods for calculating energy release rates. Eng Fract Mech 21(2): 405–421

    Article  Google Scholar 

  32. Charalambides PG, Lund J, Evans AG, McMeeking RM (1989) A test specimen for determining the fracture resistance of bimaterial interfaces. J Appl Mech 56: 77–82

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore, 117576, Singapore

    L. Chen, G. R. Liu & N. Nourbakhsh-Nia

  2. Singapore-MIT Alliance (SMA), E4-04-10, 4 Engineering Drive 3, Singapore, 117576, Singapore

    G. R. Liu

  3. Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore, 117576, Singapore

    K. Zeng

Authors
  1. L. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. R. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Nourbakhsh-Nia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, L., Liu, G.R., Nourbakhsh-Nia, N. et al. A singular edge-based smoothed finite element method (ES-FEM) for bimaterial interface cracks. Comput Mech 45, 109–125 (2010). https://doi.org/10.1007/s00466-009-0422-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-009-0422-3

Keywords

Search

Navigation