Numerical Calculation of Generalized Energy Balance Integrals

  • Meinhard KunaEmail author
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 201)


Based on Eshelby’s pioneer work [1, 2], who investigated thermodynamic forces acting on defects in solids by introducing the energy-momentum tensor, a new theory of generalized \(\tiny {\gg }\)material\(\tiny {\ll }\) or \(\tiny {\gg }\)configurational\(\tiny {\ll }\) forces has been developed in the past 15 years (see Maugin [3], Kienzler, Herrmann [4,5], and Gurtin [6]).


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  1. 1.
    Eshelby JD (1970) Energy relations and the energy momentum tensor in continuum mechanics. In: Kanninen MF (ed) Inelastic behavior of solids. McGraw Hill, New York, pp 77–114Google Scholar
  2. 2.
    Eshelby JD (1975) The elastic energy-momentum tensor. J Elast 5:321–335MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Maugin GA (1993) Material inhomogeneities in elasticity. Chapman & Hall, LondonzbMATHGoogle Scholar
  4. 4.
    Kienzler R (1993) Konzepte der Bruchmechanik. Vieweg, WiesbadenGoogle Scholar
  5. 5.
    Kienzler R, Herrmann G (2000) Mechanics in material space. With application to defects and fracture mechanics. Springer, Berlin u.aGoogle Scholar
  6. 6.
    Gurtin ME (2000) Configurational forces as basic concept of continuum physics. Springer, Berlin u. aGoogle Scholar
  7. 7.
    Shih CF, Moran B, Nakamura T (1986) Energy release rate along a three-dimensional crack front in a thermally stressed body. Int J Fract 30:79–102Google Scholar
  8. 8.
    Aoki S, Kishimoto K, Sakata S (1982) Elastic-plastic analysis of crack in thermally-loaded structures. Eng Fract Mech 16:405–413CrossRefGoogle Scholar
  9. 9.
    Wilson WK, Yu IW (1979) The use of the \(J\)-integral in thermal stress crack problems. Int J Fract 15:377–387Google Scholar
  10. 10.
    Atluri SN (1986) Computational methods in the mechanics of fracture. Elsevier Science Publisher, Noorth-HollandzbMATHGoogle Scholar
  11. 11.
    Gurtin ME (1979) On a path-independent integral for thermoelasticity. Int J Fract 15:R169–R170Google Scholar
  12. 12.
    Nishioka T, Atluri SN (1983) Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics. Eng Fract Mech 18:1–22Google Scholar
  13. 13.
    Ishikawa H, Kitagawa H, Okamura H (1980) J-integral of mixed mode crack and its application. In: Proceedings of 3rd international conference on mechanical behaviour of materials, vol 3. Pergamon Press, pp 447–455Google Scholar
  14. 14.
    Stern M, Becker EB, Dunham RS (1976) Contour integral computation of mixed-mode stress intensity factors. Int J Fract 12(3):359–368Google Scholar
  15. 15.
    Yau J, Wang S, Corton H (1980) A mixed-mode crack analysis of isotropic solids using conservation laws of elastics. J Appl Mech 47:335–341zbMATHCrossRefGoogle Scholar
  16. 16.
    Larsson SG, Carlsson AJ (1973) Influence of non-singular stress terms and specimen geometry on small-scale yielding at track tips in elastic-plastic materials. J Mech Phys Solids 21:263–277CrossRefGoogle Scholar
  17. 17.
    Leevers PS, Radon JC (1982) Inherent stress biaxiality in various fracture specimen geometries. Int J Fract 19:311–325CrossRefGoogle Scholar
  18. 18.
    Fett T (1998) A compendium of T-stress solutions. Technical report. Report FZKA 6057, Forschungszentrum Karlsruhe, Technik und UmweltGoogle Scholar
  19. 19.
    Kfouri AP (1986) Some evaluations of the elastic T-term using Eshelby’s method. Int J Fract 30:301–315CrossRefGoogle Scholar
  20. 20.
    Nakamura T, Parks DM (1992) Determination of elastic T-stress along threedimensional crack fronts using an interaction integral. Int J Solids Struct 29:1597–1611zbMATHCrossRefGoogle Scholar
  21. 21.
    Chen YZ (1985) New path independent integrals in linear elastic fracture mechanics. Eng Fract Mech 22:673–686CrossRefGoogle Scholar
  22. 22.
    Chen CS, Krause R, Pettit RG, Banks-Sills L, Ingraffea AR (2001) Numerical assessment of T-stress computation using a P-version finite element method. Fatigue Fract Eng Mater Struct 107:177–199Google Scholar
  23. 23.
    Peters B, Barth FJ, Hahn HG (1995) Klassifizierung von angerissenen Bauteilen mit Hilfe der T-Spannung. In: Tagungsband zur 27. Vortragsveranstaltung des DVM-Arbeitskreises BruchvorgängeGoogle Scholar
  24. 24.
    Tada H, Paris P, Irwin G (1985) The stress analysis of cracks handbook, 2nd edn. Paris Production Inc., St.LouisGoogle Scholar
  25. 25.
    Bahr A, Balke H, Kuna M, Liesk H (1987) Fracture analysis of a single edge cracked strip under thermal shock. Theor Appl Fract Mech 8:33–39CrossRefGoogle Scholar
  26. 26.
    Abaqus: ABAQUS theory and user manual. Dassault SystFmes Simulia Corp., Pawtucket (2010)Google Scholar
  27. 27.
    Enderlein M, Ricoeur A, Kuna M (2003) Comparison of finite element techniques for 2D and 3D crack analysis under impact loading. Int J Solids Struct 40:3425–3437zbMATHCrossRefGoogle Scholar
  28. 28.
    Eischen JW (1987) Fracture of nonhomogeneous materials. Int J Fract 34:3–22Google Scholar
  29. 29.
    Kim JH, Paulino GH (2002) Finite element evaluation of mixed mode stress intensity factors in functionally graded materials. Int J Numer Methods Eng 52:1903–1935CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute für Mechanik und FluiddynamikTU Bergakademie FreibergFreibergGermany

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