Quasistatic brittle fracture in inhomogeneous media and iterated conformal maps: Modes I, II, and III

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 6, 2002, Pages 11-

  Barra, Felipe ^a   Levermann, Anders ^a   Procaccia, Itamar ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BRITTLENESS; CRACKS; FUNCTIONS; ITERATIVE METHODS; MAPS; QUENCHING; STRESS ANALYSIS;

ANALYTIC FUNCTIONS; CONFORMAL MAPS; LAPLACE EQUATIONS; QUASISTATIC FRACTURE;

FRACTURE;

ARTICLE;

EID: 41349085330     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.066122     Document Type: Article

References (20)

1. L.D. Landau and E.M. Lifshitz, Theory of Elasticity, 3rd ed. (Pergamon, London, 1986).
2. N.I. Muskhelishvili, Some Basic Problems in the Mathematical Theory of Elasticity (Noordhoff, Groningen, 1952).
3. H.J. Herrmann and S. Roux, Statistical Models for the Fracture of Disordered Media (North-Holland, Amsterdam, 1990), and references therein.
4. J. Fineberg and M. Marder, Phys. Rep. 313, 1 (1999), and references therein.
5. L.B. Freund, Dynamic Fracture Mechanics (Cambridge University Press, Cambridge, 1998).
6. M. Barber, J. Donley, and J.S. Langer, Phys. Rev. A 40, 366 (1989).
7. See for example, J. Kertész in Ref. 3.
8. E. Louis and F. Guinea, Europhys. Lett. 3, 871 (1987).
9. See, for example, Ref. 4, Sec. II C. There is no universal agreement on the experimental velocity law, and other choices can be made here.
10. F. Barra, B. Davidovitch, A. Levermann, and I. Procaccia, Phys. Rev. Lett. 87, 134501 (2001).
11. F. Barra, B. Davidovitch, and I. Procaccia, Phys. Rev. E (to be published), e-print cond-mat/0105608.
12. F. Barra, H.G.E. Hentschel, A. Levermann, and I. Procaccia, Phys. Rev. E 65, R045101 (2002).
13. S. Ramanathan, D. Ertaş, and D.S Fisher, Phys. Rev. Lett. 79, 873 (1997).
14. M.B. Hastings and L.S. Levitov, Physica D 116, 244 (1998).
15. B. Davidovitch, H.G.E. Hentschel, Z. Olami, I. Procaccia, L.M. Sander, and E. Somfai, Phys. Rev. E 59, 1368 (1999).
16. Z. Olami, I. Procaccia, and R. Zeitak, Phys. Rev. E 52, 3402 (1995).
17. E. Bouchaud, J. Phys.: Condens. Matter 9, 4319 (1997).
18. A. Parisi, G. Caldarelli, and L. Pietronero, e-print cond-mat/0004374.
19. B. Cottrell and J.R. Rice, Int. J. Fract. 16, 155 (1980).
20. E. Bouchaud, J.P. Bouchaud, D.S. Fisher, S. Ramanathan, and J.R. Rice, J. Mech. Phys. Solids 50, 1703 (2002).