Quasistatic fractures in brittle media and iterated conformal maps

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 65, Issue 4, 2002, Pages

  Barra, Felipe ^a   George, H ^a   Hentschel, E ^a,b   Levermann, Anders ^a   Procaccia, Itamar ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b EMORY UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTIC STRAIN TENSOR; LAMÉ EQUATION; LAPLACE'S EQUATION; RACK INTERFACE;

CONFORMAL MAPPING; CRACKS; CRYSTAL LATTICES; ELASTICITY; FRACTURE MECHANICS; ITERATIVE METHODS; LAPLACE TRANSFORMS; PROBLEM SOLVING; STRAIN; SURFACE ROUGHNESS;

BRITTLENESS;

EID: 41349113974     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.045101     Document Type: Article

References (22)

1. N.I. Muskhelishvili, Some Basic Problems in the Mathematical Theory of Elasticity (Noordhoff, Groningen, 1952).
2. L.D. Landau and E.M. Lifshitz, Theory of Elasticity, 3rd ed. (Pergamon, London, 1986).
3. J. Fineberg and M. Marder, Phys. Rep. 313, 1 (1999), and references therein.
4. H.J. Herrmann and S. Roux, Statistical Models for the Fracture of Disordered Media (North-Holland, Amsterdam, 1990), and references therein.
5. L. Slepian, Dokl. Akad. Nauk. SSSR 258, 561 (1981) [Sov. Phys. Dokl. 26, 538 (1981)].
6. L. Slepian, Dokl. Akad. Nauk. SSSR 258, 561 (1981) [Sov. Phys. Dokl. 26, 538 (1981)].
7. M. Marder and X. Liu, Phys. Rev. Lett. 71, 2417 (1993).
8. A. Parisi, G. Caldarelli, and L. Pietronero, e-print arXiv:cond-mat/ 0004374.
9. M.B. Hastings and L.S. Levitov, Physica D 116, 244 (1998).
10. B. Davidovitch, H.G.E. Hentschel, Z. Olami, I. Procaccia, L.M. Sander, and E. Somfai, Phys. Rev. E 59, 1368 (1999).
11. B. Davidovitch, M.J. Feigenbaum, H.G.E. Hentschel, and I. Procaccia, Phys. Rev. E 62, 1706 (2000).
12. B. Davidovitch, A. Levermann, and I. Procaccia, Phys. Rev. E 62, R5919 (2000).
13. M. Barber, J. Donley, and J.S. Langer, Phys. Rev. A 40, 366 (1989).
14. See, for example, J. Kertész in [4].
15. E. Louis and F. Guinea, Europhys. Lett. 3, 871 (1987).
16. F. Barra, B. Davidovitch, and I. Procaccia, e-print cond-mat/0105608; Phys. Rev. E (to be published).
17. F. Barra, B. Davidovitch, and I. Procaccia, e-print cond-mat/0105608; Phys. Rev. E (to be published).
18. F. Barra, A. Levermann, and I. Procaccia (unpublished).
19. See, for example, Ref. [3], Sec. 2.3. There is no universal agreement on the experimental velocity law, and other choices can be made here.
20. Z. Olami, I. Procaccia, and R. Zeitak, Phys. Rev. E 52, 3402 (1995).
21. E. Bouchaud, J. Phys.: Condens. Matter 9, 4319 (1997).
22. S. Ramanathan, D. Ertaş, and D. S Fisher, Phys. Rev. Lett. 79, 873 (1997).