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Macroscopic fracture characteristics of random particle systems

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Abstract

This paper deals with determination of macroscopic fracture characteristics of random particle systems, which represents a fundamental but little explored problem of micromechanics of quasibrittle materials. The particle locations are randomly generated and the mechanical properties are characterized by a triangular softening force-displacement diagram for the interparticle links. An efficient algorithm, which is used to repetitively solve large systems, is developed. This algorithm is based on the replacement of stiffness changes by inelastic forces applied as external loads. It makes it possible to calculate the exact displacement increments in each step without iterations and using only the elastic stiffness matrix. The size effect method is used to determine the dependence of the mean macroscopic fracture energy and the mean effective process zone size of two-dimensional particle systems on the basic microscopic characteristics such as the microscopic fracture energy, the dominant inhomogeneity spacing (particle size) and the coefficients of variation of the microstrength and the microductility. Some general trends are revealed and discussed.

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References

  1. P.A. Cundall, in Proceedings, International Symposium on Rock Fracture, ISRM, Nancy (1971).

  2. A.A. Serrano and J.M. Rodriquez-Ortiz, in Proceedings, Symposium on Plasticity and Soil Mechanics, Cambridge, U.K. (1973).

  3. J.M. Rodriguez-Ortiz, thesis, Universidad Politecnico de Madrid, Spain (1974) in Spanish.

  4. T. Kawai, International Journal for Numerical Methods in Engineering 16 (1980) 81–120.

    Google Scholar 

  5. P.A. Cundall, BALL-A program to model granular media using the distinct element method. Technical note, Dames and Moore, London (1978).

    Google Scholar 

  6. P.A. Cundall and O.D.L. Strack, Geotechnique 29 (1979) 47–65.

    Google Scholar 

  7. A. Zubelewicz, thesis, Technical University of Warsaw, Poland (1990) in Polish.

  8. A. Zubelewicz, Archiwum Inzynierii Ladowej 29 (1983) 417–429, in Polish.

    Google Scholar 

  9. A. Zubelewicz and Z. Mróz, Rock Mechanics and Engineering 16 (1983) 253–274.

    Google Scholar 

  10. M.E. Plesha and E.C. Aifantis, in Proceedings, 24th U.S. Symposium on Rock Mechanics, College Station, Texas (1983).

  11. A. Zubelewicz and Z.P. Bažant, Journal of Engineering Mechanics ASCE 113 (1987) 1619–1630.

    Google Scholar 

  12. Z.P. Bažant, M.R. Tabbara, M.T. Kazemi and G. Pijaudier-Cabot, Journal of Engineering Mechanics ASCE 116 (1990) 1686–1705.

    Google Scholar 

  13. J.C. Charmet, S. Roux and E. Guyon (eds.), Disorder and Fracture, Plenum Press, New York (1990).

    Google Scholar 

  14. H.J. Herrmann, Fracture Processes in Concrete, Rock and Ceramics, Chapman & Hall, New York (1991).

    Google Scholar 

  15. H.J. Herrman and S. Roux (eds.), Statistical Models for the Fracture of Disordered Media, North-Holland, New York (1990).

    Google Scholar 

  16. E. Schlangen and J.G.M.van Mier, Cement and Concrete Composites 14 (1992) 105–118.

    Google Scholar 

  17. J.G.M. van Mier and E. Schlangen, Journal of the Mechanical Behavior of Materials 4 (1993) 179–190.

    Google Scholar 

  18. E. Schlangen, PhD. thesis, Technical University of Delft, The Netherlands (1993).

  19. E. Schlangen and J.G.M. van Mier, in Proceedings of Computational Methods in Materials Science, Materials Research Society, Pittsburgh, Pennsylvania (1993) 153–158.

  20. Z.P. Bažant, in SEM-RILEM International Conference on Fracture of Concrete and Rock, Houston, Texas, S.P. Shah and S.E. Swartz (eds.), SEM (1987) 390–402.

  21. Z.P. Bažant and P.A. Pfeiffer, ACI Materials Journal 84 (1987) 463–480.

    Google Scholar 

  22. H.G. Tattersall and G. Tappin, Journal of Materials Science 1:3 (1966) 296–301.

    Google Scholar 

  23. J. Nakayama, Journal of the American Ceramic Society 48:11 (1965).

    Google Scholar 

  24. A. Hillerborg, M. Modéer and P.E. Petersson, Cement and Concrete Research 6 (1976) 773–782.

    Google Scholar 

  25. Z.P. Bažant (ed.), Fracture Mechanics of Concrete Structures, Elsevier, London (1992).

    Google Scholar 

  26. Z.P. Bažant and V. Gopalaratnam, in Fracture Mechanics of Concrete Structures, Z.P. Bažant (ed.), Elsevier, London (1992) 1–140.

    Google Scholar 

  27. Z.P. Bažant and M.T. Kazemi, in Conference on Advances in Cement Manufacturing and Use, E. Gartner (ed.), (1988) Paper No. 5.

  28. Z.P. Bažant and L. Cedolin, Stability of Structures, Oxford University Press, New York (1991).

    Google Scholar 

  29. Z.P. Bažant, J.-K. Kim and P.A. Pfeiffer, Journal of Structural Engineering ASCE 112, ST2 (1986) 289–307.

    Google Scholar 

  30. Z.P. Bažant, Journal of Engineering and Mechanics ASCE 110 (1984) 518–535.

    Google Scholar 

  31. Z.P. Bažant, Materials and Structures 23 (1990) 461–465.

    Google Scholar 

  32. C. Jirásek and Z.P. Bažant, Journal of Engineering Mechanics ASCE, in press.

  33. C. Moukarzel and H.J. Herrmann, HLRZ 1/92, HLRZ KFA Jülich, Germany (1992) preprint.

  34. J.G.M. van Mier, Cement and Concrete Research 21 (1991) 1–15.

    Google Scholar 

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Authors and Affiliations

  1. Northwestern University, 60208, Evanston, Illinois, USA

    Milan Jirásek & Zdeněk P. Bažant

Authors
  1. Milan Jirásek
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  2. Zdeněk P. Bažant
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Walter P. Murphy Professor of Civil Engineering and Materials Science.

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Jirásek, M., Bažant, Z.P. Macroscopic fracture characteristics of random particle systems. Int J Fract 69, 201–228 (1994). https://doi.org/10.1007/BF00034763

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  • DOI: https://doi.org/10.1007/BF00034763

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