The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2339–2351 | Cite as

Cracks in random brittle solids:

From fiber bundles to continuum mechanics
  • S. Patinet
  • D. Vandembroucq
  • A. Hansen
  • S. Roux
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications


Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.


Critical Load European Physical Journal Special Topic Energy Release Rate Continuum Limit Fracture Process Zone 
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.
    A. Griffith, Phil. Trans. Roy. Soc. London CCXXI-A, 163 (1920)Google Scholar
  2. 2.
    W. Weibull, ASME J. Appl. Mech. 18, 293 (1951)zbMATHGoogle Scholar
  3. 3.
    P. Forquin, F. Hild, Adv. Appl. Mech. 44, 1 (2010)CrossRefGoogle Scholar
  4. 4.
    G.A. Francfort, J.-J. Marigo, Eur. J. Mech. A/Solids 12, 149 (1993)MathSciNetzbMATHGoogle Scholar
  5. 5.
    G.A. Francfort, J.-J. Marigo, J. Mech. Phys. Solids 46, 1319 (1998)MathSciNetCrossRefzbMATHADSGoogle Scholar
  6. 6.
    G.I. Barenblatt, Adv. Appl. Mech. 7, 55 (1962)MathSciNetCrossRefGoogle Scholar
  7. 7.
    D. Leguillon, C. R. Acad. Sci. Paris II-309, 945 (1990)Google Scholar
  8. 8.
    L. de Arcangelis, S. Redner, H.J. Herrmann, J. de Phys. Lett. 46, 585 (1985)CrossRefGoogle Scholar
  9. 9.
    B. Kahng, G.G. Batrouni, S. Redner, L. de Arcangelis, H.J. Herrmann, Phys. Rev. B 37, 7625 (1988)CrossRefADSGoogle Scholar
  10. 10.
    H.J. Herrmann, A. Hansen, S. Roux, Phys. Rev. B 39, 637 (1989)CrossRefADSGoogle Scholar
  11. 11.
    P. Barai, P.K.V.V. Nukala, M.J. Alava, S. Zapperi, Phys. Rev. E 88, 042411 (2013)CrossRefADSGoogle Scholar
  12. 12.
    F.T. Peirce, J. Textile Industry 17, 355 (1926)CrossRefGoogle Scholar
  13. 13.
    H.E. Daniess, Proc. Roy. Soc. London. Series A. 183, 405 (1945)CrossRefADSGoogle Scholar
  14. 14.
    P.C. Hemmer, A. Hansen, J. Appl. Mech. 59, 909 (1992)CrossRefzbMATHADSGoogle Scholar
  15. 15.
    S. Pradhan, A. Hansen, B.K. Chakrabarti, Rev. Mod. Phys. 82, 499 (2010)CrossRefADSGoogle Scholar
  16. 16.
    A. Hansen, P.C. Hemmer, S. Pradhan, The fiber bundle (Wiley, New York, 2015) (to appear)Google Scholar
  17. 17.
    D.G. Harlow, S.L. Phoenix, J. Mech. Phys. Solids 39, 173 (1991)CrossRefzbMATHADSGoogle Scholar
  18. 18.
    M. Kloster, A. Hansen, P.C. Hemmer, Phys. Rev. E 56, 2615 (1997)CrossRefADSGoogle Scholar
  19. 19.
    A. Delaplace, S. Roux, G. Pijaudier-Cabot, Int. J. Sol. Struct. 36, 1403 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    A. Delaplace, S. Roux, G. Pijaudier-Cabot, Int. J. Fracture 95, 159 (1999)CrossRefGoogle Scholar
  21. 21.
    G.G. Batrouni, A. Hansen, J. Schmittbuhl, Phys. Rev. E 65, 036126 (2002)CrossRefADSGoogle Scholar
  22. 22.
    A. Stormo, K.S. Gjerden, A. Hansen, Phys. Rev. E 86, 025101(R) (2012)CrossRefADSGoogle Scholar
  23. 23.
    R.C. Hidalgo, Y. Moreno, F. Kun, H.J. Herrmann, Phys. Rev. E 65, 046148 (2002)CrossRefADSGoogle Scholar
  24. 24.
    O. Yewande, Y. Moreno, F. Kun, R. Hidalgo, H. Herrmann, Phys. Rev. E 68, 026116 (2003)CrossRefADSGoogle Scholar
  25. 25.
    R.C. Hidalgo, F. Kun, H.J. Herrmann, Phys. A: Stat. Mech. App. 347, 402 (2005)CrossRefGoogle Scholar
  26. 26.
    A. Delaplace, S. Roux, G. Pijaudier-Cabot, J. Eng. Mech.-ASCE 127, 646 (2001)CrossRefGoogle Scholar
  27. 27.
    M. Zaiser, P. Moretti, A. Konstantinidis, E.C. Aifantis, J. Stat. Mech., P11009 (2009)Google Scholar
  28. 28.
    M. Zaiser, P. Moretti, A. Konstantinidis, E.C. Aifantis, J. Stat. Mech., P02047 (2009)Google Scholar
  29. 29.
    M. Zaiser, J. Stat. Mech., P02024 (2011)Google Scholar
  30. 30.
    S. Zapperi, H.J. Herrmann, S. Roux, Eur. Phys. J. B 17, 131 (2000)CrossRefADSGoogle Scholar
  31. 31.
    J.R. Rice, J. Appl. Mech. 52, 571 (1985)CrossRefzbMATHADSGoogle Scholar
  32. 32.
    L. Legrand, S. Patinet, J.B. Leblond, J. Frelat, V. Lazarus, D. Vandembroucq, Int. J. Fract. 170, 67 (2011)CrossRefzbMATHGoogle Scholar
  33. 33.
    J.-F. Joanny, P.G. de Gennes, J. Chem. Phys. 81, 552 (1984)CrossRefADSGoogle Scholar
  34. 34.
    M. Kardar, Phys. Rep. 301, 85 (1998)CrossRefADSGoogle Scholar
  35. 35.
    J. Schmittbuhl, S. Roux, J.-P. Vilotte, K.J. Måløy, Phys. Rev. Lett. 78, 3888 (1998)CrossRefGoogle Scholar
  36. 36.
    R. Skoe, D. Vandembroucq, S. Roux, Int. J. Mod. Phys. C 13, 751 (2002)CrossRefADSGoogle Scholar
  37. 37.
    Y. Charles, D. Vandembroucq, F. Hild, S. Roux, J. Mech. Phys. Sol. 52, 1651 (2004)CrossRefzbMATHADSGoogle Scholar
  38. 38.
    D. Vandembroucq, R. Skoe, S. Roux, Phys. Rev. E 70, 026103 (2004)CrossRefADSGoogle Scholar
  39. 39.
    D. Dalmas, A. Lelarge, D. Vandembroucq, Phys. Rev. Lett. 101, 255501 (2008)CrossRefADSGoogle Scholar
  40. 40.
    D. Bonamy, E. Bouchaud, Phys. Rep. 498, 1 (2011)CrossRefADSGoogle Scholar
  41. 41.
    S. Patinet, D. Vandembroucq, S. Roux, Phys. Rev. Lett. 110, 165507 (2013)CrossRefADSGoogle Scholar
  42. 42.
    A. Rosso, W. Krauth, Phys. Rev. E 65, 025101(R) (2002)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Laboratoire PMMH, ESPCI/CNRS-UMR 7636/Univ. Paris 6 UPMC/Univ. Paris 7 DiderotParis Cedex 05France
  2. 2.Institutt for fysikk, NTNUTrondheimNorway
  3. 3.LMT-Cachan, ENS-Cachan/CNRS/PRES UniverSud ParisCachan CedexFrance

Personalised recommendations