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On Statistical Micromechanical Theories for Brittle Solids with Interacting Microcracks

  • J. W. Ju
Conference paper
Part of the IUTAM Symposia book series (IUTAM)

Abstract

The nonlinear mechanical responses of damaged solids due to the existence, growth, and nucleation of microdefects are of significant importance to engineers, and have been the subject of many investigations. See Krajcinovic (1989) for a literature review on damage mechanics. For brittle materials, in particular, microcracks often control overall deformation and failure mechanisms. To date, the only exact results derived for microcrack-weakened brittle solids are for dilute microcrack concentrations, where microcrack interactions are entirely neglected. These micromechanical damage models are called “Taylor’s models”. On the other hand, several approximate micromechanical analyses (“effective medium methods”) were proposed in the literature to account for interaction effects of distributed microcracks.

Keywords

Representative Volume Element Probability Density Function Compliance Matrix Brittle Solid Microcrack Density 
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.

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References

  1. 1.
    Batchelor, G. K., (1970), “The Stress System in a Suspension of Force-Free Particles”, J. Fluid. Mech., Vol. 41, pp. 545–570.CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Chen, H. S. And Acrivos, A., (1978a), “The Solution of the Equations of Linear Elasticity for an Infinite Region Containing Two Spherical Inclusions”, Int. J. Solids & Struct., Vol. 14, pp. 331–348.CrossRefMATHGoogle Scholar
  3. 3.
    Chen, H. S. And Acrivos, A., (1978b), “The Effective Elastic Moduli of Composite Materials Containing Spherical Inclusions at Non-Dilute Concentrations”, Int.J. Solids & Struct., Vol. 14, pp. 349–364.CrossRefMATHGoogle Scholar
  4. 4.
    Eringen, A. C. and Edelen, D. G. B., (1972), “On Nonlocal Elasticity”, Int. J. Eng. Sci., Vol. 10, pp. 233–248.CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Fanella, D. and Krajcinovic, D., (1988), “A Micromechanical Model for Concrete in Compression”, Eng. Fract. Mech., Vol. 29, No. 1, pp. 49–66.CrossRefGoogle Scholar
  6. 6.
    Gross, D., (1982), “Spannungsintensitatsfaktoren von Ribsystemen (Stress Intensity Factors of Systems of Cracks)”, Ing.-Arch., vol. 51, pp. 301–310(in German).CrossRefMATHGoogle Scholar
  7. 7.
    Hincii. E. J., (1977), “An Averaged-Equation Approach to Particle Interactions in a Fluid Suspension”, J. Fluid Mech., Vol. 83, pp. 695–720.CrossRefGoogle Scholar
  8. 8.
    Hori, M. and Nemat-Nasser, S., (1987), “Interacting Micro-Cracks near the Tip in the Process Zone of a Macro-Crack”, J. Mech. Phys. Solids, Vol. 35, pp. 601–629.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Horii, H. and Nemat-Nasser, S., (1983), “Overall Moduli of Solids with Microcracks: Load-Induced Anisotropy”, J. Mech. Phys. Solids, Vol. 331, pp. 155–171.CrossRefGoogle Scholar
  10. 10.
    Horii, H. and Nemat-Nasser, S., (1985), “Elastic Fields of Interacting Inhomogeneities”, Int. J. Solids & Struct., Vol. 21, pp. 731–745.CrossRefMATHGoogle Scholar
  11. 11.
    Ju, J. W., (1990), “A Micromechanical Damage Model for Uniaxially Reinforced Composites Weakened by Interfacial Arc Microcracks”, J. Appl. Mech., ASME, in press.Google Scholar
  12. 12.
    Ju, J. W. and Lee, X., (1991), “On Three-Dimensional Self-Consistent Micromechanical Damage Models for Brittle Solids. Part I: Tensile Loadings”, J. Eng. Mech., vol. 117, no. 7, pp. 1495–1515.CrossRefGoogle Scholar
  13. 13.
    Kachanov, M., (1985), “A Simple Technique of Stress Analysis in Elastic Solids with Many Cracks”, Int J. Fract., vol. 28, pp. R11–R19.Google Scholar
  14. 14.
    Kachanov, M., (1987), “Elastic Solids with Many Cracks: A Simple Method of Analysis”, Int. J. Solids & Struct., Vol. 23, pp. 23–43.CrossRefMATHGoogle Scholar
  15. 15.
    Kachanov, M. and Laures, J.-P., (1989), “Three-Dimensional Problems of Strongly Interacting Arbitrarily Located Penny-Shaped Cracks”, Int. J. of Fract., Vol. 41, pp. 289–313.CrossRefGoogle Scholar
  16. 16.
    Krajcinovic, D., (1989), “Damage Mechanics”, Mech. Mater., Vol. 8, No. 2-3 (Dec. 1989), pp. 117–197.CrossRefGoogle Scholar
  17. 17.
    Krajcinovic, D. and Fanella, D., (1986), “A Micromechanical damage Model for Concrete”, Eng. Fract. Mech., Vol. 25, pp. 585–596.CrossRefGoogle Scholar
  18. 18.
    Krajcinovic, D. and Sumarac, D., (1989), “A Mesomechanical Model for Brittle Deformation Processes: Part I”, J. Appl. Mech., Vol. 56, pp. 51–62.CrossRefGoogle Scholar
  19. 19.
    Laws, N. and Dvorak, G. J., (1987), “The Effect of Fiber Breaks and Aligned Penny-Shaped Cracks on the Stiffness and Energy Release Rates in Unidirectional Composites”, Int. J. Solids & Struct., Vol. 23, No. 9, pp. 1269–1283.CrossRefGoogle Scholar
  20. 20.
    Laws, N., Dvorak, G. J. and Hejazi, M., (1983), “Stiffness Changes in Unidirectional Composites Caused by Crack Systems”, Mech. of Mater., Vol. 2, pp. 123–137.CrossRefGoogle Scholar
  21. 21.
    Lee, X. and Ju, J. W., (1991), “On Three-Dimensional Self-Consistent Micromechanical Damage Models for Brittle Solids. Part II: Compressive Loadings”, J. Eng. Mech., vol. 117, no. 7, pp. 1516–1537.CrossRefGoogle Scholar
  22. 22.
    Sneddon, I. N. and Lowengrub, M., (1969), Crack Problems in the Classical Theory of Elasticity, John Wiley & Sons, Inc., New York.MATHGoogle Scholar
  23. 23.
    Sumarac, D. and Krajcinovic, D., (1987), “A Self-Consistent Model for Microcrack-Weakened Solids”, Mech. Mater., Vol. 6, pp. 39–52.CrossRefGoogle Scholar
  24. 24.
    Sumarac, D. and Krajcinovic, D., (1989), “A Mesomechanical Model for Brittle Deforma-tion Processes: Part II”, J. Appl. Mech., Vol. 56, pp. 57–62.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag, Berlin Heidelberg 1992

Authors and Affiliations

  • J. W. Ju
    • 1
  1. 1.Department of Civil Engineering and Operations ResearchPrinceton UniversityPrincetonUSA

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