Micromechanics of the Damage Processes

  • Dusan Krajcinovic
  • Dragoslav Sumarac
Part of the International Centre for Mechanical Sciences book series (CISM, volume 295)


The presented study focuses on the formulation of the damage models based on the actual mesostructural geometry and the kinetics of its irreversible changes. Assuming that the process is sufficiently well defined by the volume averages of the state and internal variables, the overall compliance tensor is derived using both Taylor’s and self-consistent approximations. The kinetic equations are derived from the hierarchy of toughnesses at the mesoscale in conjunction with the Griffith’s criterion.


Stress Intensity Factor Acoustic Emission Energy Barrier Uniaxial Tension Crack Opening Displacement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Krajcinovic, D.: Continuum damage mechanics, to appear in Mechanics Today.Google Scholar
  2. 2.
    Lemaitre, J. and J.L. Chaboche: Aspect phenomenologique de la rupture par endommagement, J. de Mec. Applique, 2 (1978), 317–365.Google Scholar
  3. 3.
    Stroh, A.N.: A theory of fracture of metals, Advances in Physics, 6 (1957), 418–465.ADSCrossRefGoogle Scholar
  4. 4.
    Wittmann, F.H.: Structure of concrete with respect to crack formation, in Fracture Mechanics of Concrete (Ed. F.H. Wittmann ), Elsevier, Amsterdam, 1983, 43–74.Google Scholar
  5. 5.
    Chudnovski, A.: Crack Layer Theory, Case Western Reserve Univ., NASA Contractor Report 174634, 1984.Google Scholar
  6. 6.
    Hoagland, R.H., G.T. Hahn and A.R. Rosenfield: Influence of microstructure on fracture propagation in rock, Rock Mechanics, 5 (1973), 77–106.CrossRefGoogle Scholar
  7. 7.
    Meyers, M.A.: Discussion of ‘Pressure—shear impact and the dynamic viscoplastic response of metals’ by R. W. Klopp, et al., Mech. of Mat., 4 (1985), 387–393.CrossRefGoogle Scholar
  8. 8.
    Budiansky, B. and R.J. O’Connell: Elastic moduli of a cracked solid, Int. J. Solids Struct., 12 (1976), 81–97.CrossRefMATHGoogle Scholar
  9. 9.
    Kunin, I.A.: Elastic Media with Microstructure II, Springer Verlag, Berlin 1983.CrossRefMATHGoogle Scholar
  10. 10.
    Mura, T.: Micromechanics of Defects in Solids, M. Nijhoff Publ., The Hague 1982.CrossRefGoogle Scholar
  11. 11.
    Delameter, W. and G. Herrmann: Weakening of elastic solids by doubly periodic arrays of cracks, in Topics in Applied Mechanics (Eds., J.L. Zeman and F. Ziegler ), Springer Verlag, Berlin 1974, 156–173.Google Scholar
  12. 12.
    Margolin, L.G.: Elastic moduli of a cracked body, Int. J. of Fracture, 22 (1983), 65–79.CrossRefGoogle Scholar
  13. 13.
    Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Royal Soc., A241 (1957), 376–396.MATHMathSciNetGoogle Scholar
  14. 14.
    Hoenig, A.: The behavior of a flat elliptical crack in an anisotropie body, Int. J. Solids Struct., 14 (1978), 925–934.CrossRefMATHGoogle Scholar
  15. 15.
    Wu, C.H.: Tension-compression test of a concrete specimen via damage theory, in Damage Mechanics and Continuum Modeling (Eds., N. Stubbs, D. Krajcinovic ), ASCE Publ., New York, 1985, 1–12.Google Scholar
  16. 16.
    Fanella, D.A.: A Micromechanical Continuous Damage Model for Plain Concrete, Ph. D. Thesis, Univ. of Illinois at Chicago, 1986.Google Scholar
  17. 17.
    Kanninen, M.F. and C.H. Popelar: Advanced Fracture Mechanics, Oxford Univ. Press, New York 1985.Google Scholar
  18. 18.
    Kachanov, L.M.: On the creep rupture time, Izv. AN SSSR, Otd. Tekhn. Nauk, 8 (1958), 26–31.Google Scholar
  19. 19.
    Krajcinovie, D.: Continuous damage mechanics, Applied Mech. Rev., 37 (1984), 1–6.Google Scholar
  20. 20.
    Horii, H. and S. Nemat-Nasser: Overall moduli of solids with microcracks: load induced anisotropy, J. Mech. Phys. Solids, 31 (1983), 155–171.ADSCrossRefMATHGoogle Scholar
  21. 21.
    Kanaun, S.R.: A random crack field in an elastic continuum, Isled. po Uprug. i Plast., 10 (1974), 66–83.Google Scholar
  22. 22.
    Kachanov, M.: Elastic solids with many cracks: a simple method of analysis, to appear in Int. J. Solids Struct.Google Scholar
  23. 23.
    Kachanov, M.: A microcrack model of rock inelasticity–Part I, Mech. of Materials, 1 (1982), 19–27.CrossRefGoogle Scholar
  24. 24.
    Krajcinovic, D. and D. Fanella: A micromechanical model for concrete, to appear in Eng. Fracture Mech.Google Scholar
  25. 25.
    Ashby, M.F.: Micromechanics of fracture in static and cyclic failure, in Fracture Mechanics (Ed: R.A. Smith ), Pergamon Press, Oxford 1979, 1–27.CrossRefGoogle Scholar
  26. 26.
    Broek, D.: Elementary Engineering Fracture Mechanics, Si j thoff and Noordhoff Publ., The Netherlands, 1978.MATHGoogle Scholar
  27. 27.
    Holcomb, D.J.: Using acoustic emissions to determine in-situ stress: problems and promise, in Geomechanics - AMD Vol. 57 (Ed: S. Nemat-Nasser ), ASME 1983.Google Scholar
  28. 28.
    Holcomb, D.J. and L.S. Costin: Detecting damage surfaces in brittle materials using acoustic emissions, to appear in J. Appl. Mech.Google Scholar
  29. 29.
    Sih, G.C., P.C. Paris and G.R. Irwin: On cracks in rectilinearly anisotropie bodies, Int. J. Fraet. Mech., 1 (1965), 189–203.Google Scholar
  30. 30.
    Lekhnitski, S.G.: Theory of Elasticity of an Anisotropie Body, Mir Publ., Moscow 1981.Google Scholar
  31. 31.
    Hill, R.: The essential structure of constitutive laws for metal composites and polycrystals, J. Mech. Phys. Solids, 15 (1967), 79–95.ADSCrossRefGoogle Scholar
  32. 32.
    Lemaitre, J. and J.L. Chaboche: Mecanique des Materiaux Solides, Dunod, Paris 1985.Google Scholar
  33. 33.
    Krajeinovic, D.: Continuum damage mechanics revisited: basic concepts and definitions, J. Appl. Mech., 52 (1985), 829–834.ADSCrossRefGoogle Scholar
  34. 34.
    Jansson, S. and U. Stigh: Influence of cavity shape on damage parameter, J. Appl. Mech., 52 (1985), 609–614.ADSCrossRefGoogle Scholar
  35. 35.
    Huit, J.: Effect of voids on creep rate and strength, in Damage Mechanics and Continuum Modeling (Eds., N. Stubbs and D. Krajcinovic ), ASCE Publ., New York 1985, 13–24.Google Scholar
  36. 36.
    Rudnicki, J.W.: The inception of faulting in a rock mass with a weakened zone, J. Geophys. Res., 82 (1977), 844–854.ADSCrossRefGoogle Scholar
  37. 37.
    Rudnicki, J.W. and J.R. Rice: Conditions for the localization of deformation in pressure—sensitive dilatant materials, J. Mech. Phys. Solids, 23 (1975), 371–394.ADSCrossRefGoogle Scholar
  38. 38.
    Tetelman, A.S. and A.J. McEvily, Jr.: Fracture of Structural Materials, J. Wiley and Sons, New York 1967.Google Scholar
  39. 39.
    Zaitsev, Y.: Deformation and Strength Models for Concrete Based on Fracture Mechanics, Stroiizdat, Moscow 1982.Google Scholar
  40. 40.
    Mindess, S. and J. Young: Concrete, Prentice—Hall Inc., Englewood Cliffs N.J. 1981.Google Scholar
  41. 41.
    Harr, M.E.: Mechanics of Particulate Media, McGraw Hill Co., New York 1977.Google Scholar
  42. 42.
    Gopalaratnam, V.S. and S.P. Shah: Softening response of plain concrete in direct tension, J. Am. Concrete Inst., 82 (1985), 310–323.Google Scholar
  43. 43.
    Moavenzadeh, F. and T.W. Bremner: Fracture of Portland cement concrete, in Structure, Solid Mechanics and Engineering Design (Ed., M. Te’eni ), Wiley—Interscience Publ., New York„ 1971, 997–1008.Google Scholar
  44. 44.
    Nemat—Nasser, S. and H. Horii: Compression induced non—planar crack extension with application to splitting, exfoliation and rockburst, J. Geophys. Res., 87 (1982), 6805–6821.Google Scholar
  45. 45.
    Horii, H. and S. Nemat—Nasser: Compression induced micro—crack growth in brittle solids: axial splitting and shear failure, J. Geophys. Res., 90 (1985), 3105–3125.ADSCrossRefGoogle Scholar
  46. 46.
    Davison, L., A.L. Stevens and M.E. Kipp: Theory of spell damage accumulation in ductile metals, J. Mech. Phys. Solids, 25 (1977), 11–28.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1987

Authors and Affiliations

  • Dusan Krajcinovic
    • 1
  • Dragoslav Sumarac
    • 1
  1. 1.University of IllinoisChicagoUSA

Personalised recommendations