Acta Mechanica Sinica

, Volume 16, Issue 3, pp 240–253 | Cite as

Bueckner's work conjugate integrals and weight functions for a crack in anisotropic solids

  • Chen Yiheng
  • Ma Lifeng


The Bueckner work conjugate integrals are studied for cracks in anisotropic elastic solids. The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit functional representations of the integrals are given for several typical cases. It is found that the pseudoorthogonal property of the eigenfunction expansion forms presented previously for isotropic cases, isotropic bimaterials, and orthotropic cases, are proved to be also valid in the present case of anisotropic material. Finally, Some useful path-independent integrals and weight functions are proposed.

Key Words

work conjugate integral weight function pseudo-orthogonal property eigenfunction expansion forms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chen YZ. New path independent integrals in linear elastic fracture mechanics.Engng Fract Mech, 1985, 22: 673–686CrossRefGoogle Scholar
  2. 2.
    Chen YH, Hasebe N. Further investigation of Comninou's EEF for an interface crack with completely closed faces.Int J Engng Science, 1994, 32: 1037–1046zbMATHCrossRefGoogle Scholar
  3. 3.
    Chen YZ, Hasebe N. Eigenfunction Expansion and Higher order weight functions of interface cracks.ASME J Applied Mech, 1994, 61: 843–849zbMATHCrossRefGoogle Scholar
  4. 4.
    Chen YZ, Hasebe N. Investigation of EEF properties for a crack in a plane orthotropic elastic solid with purely imaginary characteristic roots.Engng Fract Mech, 1995, 50: 249–259CrossRefGoogle Scholar
  5. 5.
    Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks.ASME J Applied Mech, 1968, 35: 379–386Google Scholar
  6. 6.
    Budiansky B, Rice JR. Conservation laws and energy release rate.ASME J Applied Mech, 1973, 40: 201–203zbMATHGoogle Scholar
  7. 7.
    Freund LB. Stress intensity factor calculation based on a conservation integral.Int J Solids Struct, 1978, 14: 241–250CrossRefGoogle Scholar
  8. 8.
    Herrmann AG, Herrmann G. On energy-release rates for a plane crack.ASME J Applied Mech, 1981, 48: 525–528zbMATHCrossRefGoogle Scholar
  9. 9.
    Hellen TK, Blackburn WS. The calculation of stress intensity factors for combined tensile and shear loading.Int J Fract, 1975, 11: 605–617CrossRefGoogle Scholar
  10. 10.
    Stern M, Becker EB, Dunham RS. A contour integral computation of mixed-mode stress intensity factors.Int J Fract, 1976, 12: 356–368Google Scholar
  11. 11.
    Bueckner HF. Field singularities and related integral representations, In: Sih GC, ed. Mechanics of Fracture, Vol. 1 Leyden: Noordhoff, 1973. 239–314Google Scholar
  12. 12.
    Sha GT, Chen JK. Weight functions for bimaterial interface cracks.Int J Fract, 1991, 51: 265–284CrossRefGoogle Scholar
  13. 13.
    Park JH, Earmme YY. Application of conservation integrals to interfacial crack problem.Mech Materials, 1986, 5: 261–276CrossRefGoogle Scholar
  14. 14.
    Knowles JK, Sternberg E. On a class of conservation laws in linearized and finite elastostatics.Arch Rot Mech Anal, 1972, 44: 187–211zbMATHMathSciNetGoogle Scholar
  15. 15.
    Kanninen MF, Popelar CH. Advanced Fracture Mechanics. New York: Oxford University Press, 1985zbMATHGoogle Scholar
  16. 16.
    Sokolnikoff S. Mathematical Theory of Elasticity. New York: McGraw-Hill, 1956zbMATHGoogle Scholar
  17. 17.
    Lekhnitskii SG. Theory of Elasticity of an Anisotropic Elastic Body. San Francisco: Holden Day Inc., 1963zbMATHGoogle Scholar
  18. 18.
    Bowie OL, Freese CE. Central crack in plane orthotropic rectangular sheet.Int J Fract Mech, 1972, 8: 49–57CrossRefGoogle Scholar
  19. 19.
    England AH. On stress singularities in linear elasticity.Int J Engng Sci, 1971, 9: 571–585zbMATHCrossRefGoogle Scholar
  20. 20.
    Obata M, Nemat-Nasser S, Goto Y. Branched cracks in anisotropic elastic solids.ASME J Applied Mech, 1989, 56: 858–864CrossRefGoogle Scholar
  21. 21.
    Miller GR, Stock WL. Analysis of branched interface cracks between dissimilar anisotropic media.ASME J Applied Mech, 1989, 56: 844–849zbMATHCrossRefGoogle Scholar
  22. 22.
    Sosa H. Plane problems problem in piezoelectric media with defects.Int J Solids Structures, 1991, 28: 491–505zbMATHCrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2000

Authors and Affiliations

  • Chen Yiheng
    • 1
  • Ma Lifeng
    • 1
  1. 1.School of Civil Engineering and MechanicsXi'an Jiaotong UniversityXi'anChina

Personalised recommendations