Abstract
By simulating two-dimensional models of electric breakdown and fracture it is possible to characterize the rupture of disordered materials subject to an increasing external stress. We provide a review of numerical and analytical results concerning the scaling properties of avalanche events prior the macroscopic breakdown of the material. The obtained results suggest a scenario that describes fractures as a firstorder phase transition in the proximity of a spinodal-like instability. Finally, we discuss the properties of the avalanche branching ratio in the present context.
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References
K. K. Bardhan, B. K. Chakrabarti and A. Hansen (eds.), Non-linearity and breakdown in soft condensed matter, (Springer Verlag, Berlin, 1994). B. K. Chakrabarti and L. G. Benguigui, Statistical physics of fracture and breakdown in disordered systems (Oxford Univ. Press, Oxford, 1997).
A. Garcimartín, A. Guarino, L. Bellon and S. Ciliberto, Phys. Rev. Lett. 79, 3202 (1997); A. Guarino, A. Garcimartín and S. Ciliberto, Eur. Phys. J. B 6, 13 (1998).
C. Maes, A. Van Moffaert, H. Frederix and H. Strauven, Phys. Rev. B 57, 4987 (1998).
A. Petri, G. Paparo, A. Vespignani, A. Alippi and M. Costantini, Phys. Rev. Lett. 73, 3423 (1994).
G. Cannelli, R. Cantelli and F. Cordero, Phys. Rev. Lett. 70, 3923 (1993).
J. Weiss and. J.-R. Grasso, J. Phys. Chem. B 101, 6113 (1997).
P. Diodati, F. Marchesoni and S. Piazza, Phys. Rev. Lett. 67, 2239 (1991).
S. Zapperi, P. Ray, H. E. Stanley and A. Vespignani, Phys. Rev. Lett. 78, 1408 (1997); Phys. Rev. E 59, 5049 (1999)
S. Zapperi, A. Vespignani and H. E. Stanley, Nature 388, 658 (1997).
L. de Arcangelis, S. Redner and H. J. Herrmann, J. Phys. Lett. (Paris) 46, L585 (1985).
P. Duxbury, P. D. Beale and P. L. Leath, Phys. Rev. Lett. 57, 1052 (1986).
L. de Arcangelis and H.J. Herrmann, Phys. Rev. B 39, 2678 (1989).
B. Kahng, G. G. Batrouni, S. Redner, L. de Arcangelis and H. J. Herrmann, Phys. Rev. B 37, 7625 (1988).
P. Ray and G. Date, Physica A 229, 26 (1996).
K.-T. Leung and J. V. Andersen, Europhys. Lett. 38 589 (1997); K.-T. Leung, J. V. Andersen and D. Sornette, Phys. Rev. Lett. 80, 1916 (1998).
C. Unger and W. Klein, Phys. Rev. B 29, 2698 (1984); ibidem 31, 6127 (1985). For a review see L. Monette, Int. J. of Mod. Phys B 8, 1417 (1994).
A. Hansen and P. C. Hemmer, Phys. Lett. A 184, 394 (1994).
P. C. Hemmer and A. Hansen, J. Appl. Mech. 59, 909 (1992); M. Kloster, A. Hansen and P. C. Hemmer Phys. Rev E 56, 2615 (1997).
S. Kirkpatrik, Rev. Mod. Phys. 45, 574 (1973).
R. L. B. Selinger, Z.-G. Wang, W. M. Gelbart and A. Ben-Saul, Phys. Rev. A 43, 4396 (1991); Z.-G. Wang, U. Landman, R. L. B. Selinger and W. M. Gelbart, Phys. Rev. B 44 378 (1991).
M. Acharaya and B. K. Chakrabarti, Phys. Rev. E 53, 140 (1996); M. Acharaya, P. Ray and B. K. Chakrabarti, Physica A 224, 287 (1996).
D. Heerman, W. Klein and D. Stauffer, Phys. Rev. Lett. 49 1262 (1982); T. Ray and W. Klein, J. Stat. Phys. 61, 891 (1990).
G. Caldarelli, C. Castellano and A. Petri, Physica A 270, 15 (1999).
Y. Moreno, J. B. Gomez, A. F. Pacheco, Phys. Rev. Lett. 85, 2865 (2000)
T. E. Harris, The Theory of Branching Processes (Dover, New York, 1989).
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Zapperi, S., Ray, P., Stanley, H.E., Vespignani, A. (2001). Avalanches and Damage Clusters in Fracture Processes. In: Reguera, D., Rubí, J.M., Bonilla, L.L. (eds) Coherent Structures in Complex Systems. Lecture Notes in Physics, vol 567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44698-2_28
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DOI: https://doi.org/10.1007/3-540-44698-2_28
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