Fracturing highly disordered materials

Physical Review Letters

Volumn 109, Issue 25, 2012, Pages

  Moreira, A A ^a   Oliveira, C L N ^a   Hansen, A ^b   Araujo N A M ^c   Herrmann, H J ^a,c   Andrade, J S ^a  

^a FEDERAL UNIVERSITY OF CEARÁ   (Brazil)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^c ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

DISORDERED MATERIALS; HETEROGENEOUS MATERIALS; INVASION PERCOLATION; NETWORK MODELS; OPTIMAL PATHS; PERCOLATION CLUSTERS; PHYSICAL MODEL; STATISTICAL ERRORS; STRONG DISORDERS; UNIVERSALITY CLASS;

FRACTAL DIMENSION; MODELS; OPTIMIZATION; SOLVENTS;

FRACTURE;

EID: 84871536250     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.109.255701     Document Type: Article

References (37)

1. M. P. Marder, Condensed Matter Physics (Wiley, Hoboken, 2010), 2nd ed.
2. M. F. Kanninen and C. H. Popelar, Advanced Fracture Mechanics, The Oxford Engineering Science Series (Oxford University, New York, 1985).
3. M. Sahimi, Phys. Rep. 306, 213 (1998). PRPLCM 0370-1573 10.1016/S0370-1573(98)00024-6
4. M. J. Alava, P. K. V. V. Nukala, and S. Zapperi, Adv. Phys. 55, 349 (2006). ADPHAH 0001-8732 10.1080/00018730300741518 (Pubitemid 43884572)
5. B. Kahng, G. G. Batrouni, S. Redner, L. de Arcangelis, and H. J. Herrmann, Phys. Rev. B 37, 7625 (1988). PRBMDO 0163-1829 10.1103/PhysRevB.37. 7625
6. P. K. V. V. Nukala, S. Simunovic, and S. Zapperi, J. Stat. Mech. Theory Exp. (2004) P08 001. JSMTC6 1742-5468 10.1088/1742-5468/2004/08/P08001
7. I. Malakhovsky and M. A. J. Michels, Phys. Rev. B 76, 144201 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.76.144201
8. D.-P. Hao, G. Tang, H. Xia, K. Han, and Z.-P. Xun, J. Stat. Phys. 146, 1203 (2012). JSTPBS 0022-4715 10.1007/s10955-012-0435-8
9. A. Hansen, E. L. Hinrichsen, and S. Roux, Phys. Rev. Lett. 66, 2476 (1991); PRLTAO 0031-9007 10.1103/PhysRevLett.66.2476
10. A. Hansen E. L. Hinrichsen S. Roux Phys. Rev. B 43, 665 (1991). PRBMDO 0163-1829 10.1103/PhysRevB.43.665
11. L. de Arcangelis, A. Hansen, H. J. Herrmann, and S. Roux, Phys. Rev. B 40, 877 (1989). PRBMDO 0163-1829 10.1103/PhysRevB.40.877
12. A. Gilabert, C. Vanneste, D. Sornette, and E. Guyon, J. Phys. (Paris) 48, 763 (1987). JOPQAG 0302-0738 10.1051/jphys:01987004805076300
13. M. J. Alava, P. K. V. V. Nukala, and S. Zapperi, Int. J. Fract. 154, 51 (2008); IJFRAP 0376-9429 10.1007/s10704-008-9306-3
14. P. K. V. V. Nukala, S. Zapperi, M. J. Alava, and S. Š imunović, Int. J. Fract. 154, 119 (2008); IJFRAP 0376-9429 10.1007/s10704-008-9298-z
15. C. Manzato, A. Shekhawat, P. K. V. V. Nukala, M. J. Alava, J. P. Sethna, and S. Zapperi, Phys. Rev. Lett. 108, 065504 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.065504
16. L. de Arcangelis, S. Redner, and H. J. Herrmann, J. Phys. (Paris), Lett. 46, 585 (1985). JPSLBO 0302-072X 10.1051/jphyslet:019850046013058500
17. F. Wittel, F. Kun, H. J. Herrmann, and B. H. Kroplin, Phys. Rev. Lett. 93, 035504 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.035504
18. T. Pardoen, F. Hachez, B. Marchioni, P. H. Blyth, and A. G. Atkins, J. Mech. Phys. Solids 52, 423 (2004). JMPSA8 0022-5096 10.1016/S0022-5096(03)00087- 5
19. E. W. Wong, P. E. Sheehan, and C. M. Lieber, Science 277, 1971 (1997). SCIEAS 0036-8075 10.1126/science.277.5334.1971 (Pubitemid 27449134)
20. The linear equation system was solved through the HSL library, a collection of FORTRAN codes for large-scale scientific computation. See http://www.hsl.rl.ac.uk/.
21. J. S. Andrade, E. A. Oliveira, A. A. Moreira, and H. J. Herrmann, Phys. Rev. Lett. 103, 225503 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.225503
22. M. Cieplak, A. Maritan, and J. R. Banavar, Phys. Rev. Lett. 72, 2320 (1994). PRLTAO 0031-9007 10.1103/PhysRevLett.72.2320
23. E. Fehr, J. S. Andrade, S. D. da Cunha, L. R. da Silva, H. J. Herrmann, D. Kadau, C. F. Moukarzel, and E. A. Oliveira, J. Stat. Mech. (2009) P09007; JSMTC6 1742-5468 10.1088/1742-5468/2009/09/P09007
24. E. Daryaei, N. A. M. Araújo, K. J. Schrenk, S. Rouhani, and H. J. Herrmann, Phys. Rev. Lett. 109, 218701 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.218701
25. E. A. Oliveira, K. J. Schrenk, N. A. M. Araújo, H. J. Herrmann, and J. S. Andrade, Phys. Rev. E 83, 046113 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.83.046113
26. N. A. M. Araújo and H. J. Herrmann, Phys. Rev. Lett. 105, 035701 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.035701
27. M. Cieplak, A. Maritan, and J. R. Banavar, Phys. Rev. Lett. 76, 3754 (1996). PRLTAO 0031-9007 10.1103/PhysRevLett.76.3754
28. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 1992).
29. S. Roux, A. Hansen, H. Herrmann, and E. Guyon, J. Stat. Phys. 52, 237 (1988). JSTPBS 0022-4715 10.1007/BF01016411
30. E. Fehr, D. Kadau, N. A. M. Araújo, J. S. Andrade, and H. J. Herrmann, Phys. Rev. E 84, 036116 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84. 036116
31. M. Porto, S. Havlin, S. Schwarzer, and A. Bunde, Phys. Rev. Lett. 79, 4060 (1997); PRLTAO 0031-9007 10.1103/PhysRevLett.79.4060
32. M. Porto, N. Schwartz, S. Havlin, and A. Bunde, Phys. Rev. E 60, R2448 (1999). PLEEE8 1063-651X 10.1103/PhysRevE.60.R2448
33. K. J. Schrenk, N. A. M. Araújo, J. S. Andrade, and H. J. Herrmann, Sci. Rep. 2, 348 (2012). 2045-2322 10.1038/srep00348
34. D. Wilkinson and J. F. Willemsen, J. Phys. A 16, 3365 (1983). JPHAC5 0305-4470 10.1088/0305-4470/16/14/028
35. S. Roux and E. Guyon, J. Phys. A 22, 3693 (1989). JPHAC5 0305-4470 10.1088/0305-4470/22/17/034
36. A. P. Sheppard, M. A. Knackstedt, W. V. Pinczewski, and M. Sahimi, J. Phys. A 32, L521 (1999). JPHAC5 0305-4470 10.1088/0305-4470/32/49/101
37. A. Shekhawat, S. Zapperi, and J. P. Sethna, arXiv:1210.0989.