- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Crossover behavior in a mixed-mode fiber bundle model

Srutarshi Pradhan1,*, Bikas K. Chakrabarti2,†, and Alex Hansen1,‡

  • 1Department of Physics, Norwegian University of Science and Technology, Trondheim 7491, Norway
  • 2Condensed Matter Physics Group, Saha Institute of Nuclear Physics, 1/AF, Bidhan Nagar, Kolkata 700 064, India

  • *Electronic address: pradhan.srutarshi@phys.ntnu.no
  • †Electronic address: bikas@cmp.saha.ernet.in
  • ‡Electronic address: alex.hansen@phys.ntnu.no
PDF

Phys. Rev. E 71, 036149 – Published 29 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.036149

Abstract

We introduce a mixed-mode load sharing scheme in a fiber bundle model. This model reduces exactly to equal-load-sharing (ELS) and local-load-sharing (LLS) models at the two extreme limits of a single-load-sharing parameter. We identify two distinct regimes: (a) the mean-field regime where the ELS mode dominates and (b) the short-range regime dominated by the LLS mode. The crossover behavior is explored through a numerical study of the strength variation, the avalanche statistics, susceptibility and relaxation time variations, the correlations among the broken fibers, and their cluster analysis. Analyzing the moments of the cluster size distributions we locate the crossover point of these regimes. We thus conclude that even in one dimension, the fiber bundle model shows crossover behavior from mean-field to short-range interactions.

View figure in article

Article Text

References (31)

  1. Statistical Models for the Fracture of Disordered Media, edited by H. J. Herrmann and S. Roux (North-Holland, Amsterdam, 1990); B. K. Chakrabarti and L. G. Benguigui, Statistical Physics of Fracture and Breakdown in Disorder Systems (Oxford University Press, Oxford, 1997); M. Sahimi, Heterogeneous Materials II: Nonlinear and Breakdown Properties (Springer-Verlag, New York, 2003).
  2. F. T. Peirce, J. Text. Inst. 17, T355 (1926).
  3. H. E. Daniels, Proc. R. Soc. London, Ser. A 183, 405 (1945).
  4. B. D. Coleman, J. Appl. Phys. 27, 862 (1956); Trans. Soc. Rheol. 1, 153 (1957); 2, 195 (1958).
  5. W. I. Newman and S. L. Phoenix, Phys. Rev. E 63, 021507 (2000).
  6. S. Roux, Phys. Rev. E 62, 6164 (2000); R. Scorretti, S. Ciliberto, and A. Guarino, Europhys. Lett. 55, 626 (2001).
  7. S. Pradhan and B. K. Chakrabarti, Phys. Rev. E 67, 046124 (2003).
  8. P. C. Hemmer and A. Hansen, J. Appl. Mech. 59, 909 (1992).
  9. A. Hansen and P. C. Hemmer, Phys. Lett. A 184, 394 (1994).
  10. M. Kloster, A. Hansen, and P. C. Hemmer, Phys. Rev. E 56, 2615 (1997).
  11. D. Sornette, J. Phys. A 22, L243 (1989); J. Phys. I 2, 2089 (1992); A. T. Bernardes and J. G. Moreira, Phys. Rev. B 49, 15035 (1994).
  12. S. Zapperi, P. Ray, H. E. Stanley, and A. Vespignani, Phys. Rev. Lett. 78, 1408 (1997).
  13. Y. Moreno, J. B. Gomez, and A. F. Pacheco, Phys. Rev. Lett. 85, 2865 (2000).
  14. R. da Silveira, Am. J. Phys. 67, 1177 (1999).
  15. S. Pradhan and B. K. Chakrabarti, Phys. Rev. E 65, 016113 (2001).
  16. S. Pradhan, P. Bhattacharyya, and B. K. Chakrabarti, Phys. Rev. E 66, 016116 (2002).
  17. P. Bhattacharyya, S. Pradhan, and B. K. Chakrabarti, Phys. Rev. E 67, 046122 (2003).
  18. D. G. Harlow and S. L. Phoenix, J. Compos. Mater. 12, 314 (1978); R. L. Smith, Adv. Appl. Probab. 15, 304 (1982).
  19. S. L. Phoenix, Adv. Appl. Probab. 11, 153 (1979); R. L. Smith and S. L. Phoenix, J. Appl. Mech. 48, 75 (1981).
  20. S. L. Phoenix and R. L. Smith, Int. J. Solids Struct. 19, 479 (1983).
  21. R. L. Smith, Proc. R. Soc. London, Ser. A 372, 539 (1980).
  22. J. B. Gomez, D. Iniguez, and A. F. Pacheco, Phys. Rev. Lett. 71, 380 (1993).
  23. S. Pradhan and B. K. Chakrabarti, Int. J. Mod. Phys. B 17, 5565 (2003).
  24. A. Hansen and P. C. Hemmer, Trends Stat. Phys. 1, 213 (1994).
  25. R. C. Hidalgo, Y. Moreno, F. Kun, and H. J. Herrmann, Phys. Rev. E 65, 046148 (2002).
  26. A. Garcimartin, A. Guarino, L. Bellon, and S. Ciliberto, Phys. Rev. Lett. 79, 3202 (1997).
  27. A. Guarino, A. Garcimartin, and S. Ciliberto, Eur. Phys. J. B 6, 13 (1998).
  28. A. Petri, G. Paparo, A. Vespignani, A. Alippi, and M. Costantini, Phys. Rev. Lett. 73, 3423 (1994).
  29. M. Acharyya and B. K. Chakrabarti, Physica A 224, 254 (1996).
  30. G. D. Langer, R. C. Hidalgo, F. Kun, Y. Moreno, S. Aicher, and H. J. Herrmann, Physica A 325, 547 (2003).
  31. R. Stnchcombe, in Phase Transition and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, New York, 1983).

Outline

Information

Phys. Rev. E 71, 036149– Published 29 March, 2005
  • Received 19 May 2004

© 2005 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation