Planar cracks in the fuse model

European Physical Journal B

Volumn 17, Issue 1, 2000, Pages 131-136

  Zapperi, S ^a,b   Herrmann, H J ^b   Roux, S ^c  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b ESPCI   (France)

^c Lab Surf du Verre et Interfaces B   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040522578     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510070168     Document Type: Article

References (33)

1. B.B. Mandelbrot, D.E. Passoja, A.J. Paullay, Nature (London) 308, 721 (1984).
2. For a review see E. Bouchaud, J. Phys. C 9, 4319 (1997).
3. J. Schmittbuhl, K. Måløy, Phys. Rev. Lett. 78, 3888 (1997); A. Delaplace, J. Schmittbuhl, K.J. Måløy, Phys. Rev. E 60, 1337 (1999).
4. J. Schmittbuhl, K. Måløy, Phys. Rev. Lett. 78, 3888 (1997); A. Delaplace, J. Schmittbuhl, K.J. Måløy, Phys. Rev. E 60, 1337 (1999).
5. H. Gao, J.R. Rice, ASME J. Appl. Mech. 56, 828 (1989).
6. T. Nattermann, S. Stepanow, L.H. Tang, H. Leschhorn, J. Phys. II France 2, 1483 (1992).
7. O. Narayan, D.S. Fisher, Phys. Rev. B 48, 7030 (1993).
8. S. Ramanathan, D. Ertaş, D.S. Fisher, Phys. Rev. Lett. 79, 873 (1997).
9. J. Schmittbuhl, S. Roux, J.P. Vilotte, K.J. Måløy, Phys. Rev. Lett. 74, 1787 (1995); A. Tanguy, M. Gounelle, S. Roux, Phys. Rev. E 58, 1577-1590 (1998).
10. J. Schmittbuhl, S. Roux, J.P. Vilotte, K.J. Måløy, Phys. Rev. Lett. 74, 1787 (1995); A. Tanguy, M. Gounelle, S. Roux, Phys. Rev. E 58, 1577-1590 (1998).
11. S. Ramanathan, D. Fisher, Phys. Rev. Lett. 79, 877 (1997); Phys. Rev. B 58, 6026 (1998).
12. S. Ramanathan, D. Fisher, Phys. Rev. Lett. 79, 877 (1997); Phys. Rev. B 58, 6026 (1998).
13. Statistical Models for the Fracture of Disordered Media edited by H.J. Herrmann, S. Roux (North Holland, Amsterdam, 1990).
14. L. de Arcangelis, S. Redner, H.J. Herrmann, J. Phys. Lett. France 46, L585 (1985).
15. P. Duxbury, P.D. Beale, P.L. Leath, Phys. Rev. Lett. 57, 1052 (1986).
16. L. de Arcangelis, H.J. Herrmann, Phys. Rev. B 39, 2678 (1989).
17. B. Kahng, G.G. Batrouni, S. Redner, L. de Arcangelis, H.J. Herrmann, Phys. Rev. B 37, 7625 (1988).
18. A. Hansen, P.C. Hemmer, Phys. Lett. A 184, 394 (1994).
19. F. Tzschichholz, H.J. Herrmann, Phys. Rev. E 51, 1961 (1995).
20. S. Zapperi, P. Ray, H.E. Stanley, A. Vespignani, Phys. Rev. Lett. 78, 1408 (1997).
21. G. Caldarelli, F. Di Tolla, A. Petri, Phys. Rev. Lett. 77, 2503 (1996)
22. S. Zapperi, A. Vespignani, H.E. Stanley, Nature 388, 658 (1997).
23. A. Hansen, E.L. Hinrichsen, S. Roux, Phys. Rev. Lett. 66, 2476 (1991).
24. G. Caldarelli, R. Cafiero, A. Gabrielli, Phys. Rev. E 57, 3878 (1998).
25. V.I. Raisanen, E.T. Seppala, M.J. Alava, P.M. Duxbury, Phys. Rev. Lett. 80, 329 (1998).
26. G.G. Batrouni, A. Hansen, Phys. Rev. Lett. 80, 325 (1998).
27. A. Parisi, G. Caldarelli, A. Pietronero, preprint cond-mat/0004347.
28. T. Fukuhara, H. Nakanishi, J. Phys. Soc. Jpn 67, 4064 (1998).
29. B. Sapoval, M. Rosso, J.F. Gouyet, J. Phys. Lett. France 46, L149 (1985).
30. -7.
31. We have dropped the unitary horizontal conductivity.
32. 4.
33. The inclusion of bending forces, which are absent in the fuse model, could change the main features of the problem. It has recently been shown that the damage ahead of the crack is irrelevant also in this case. J. Åström, M.J. Alava and J. Timonen, unpublished.