Self-consistent scheme for toughness homogenization

International Journal of Fracture

Volumn 154, Issue 1-2, 2008, Pages 159-166

  Roux, Stéphane ^a   Hild, François ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Brittle fracture; Homogenization; Random toughness; Self consistent scheme

Indexed keywords

BRITTLENESS; DIRECT NUMERICAL SIMULATION; DISTRIBUTION FUNCTIONS; PROBABILITY DISTRIBUTIONS;

A PLANES; HOMOGENIZATION; HOMOGENIZATION SCHEMES; MEAN VALUES; PLANAR CRACKS; PROBABILITY DISTRIBUTION FUNCTIONS; RANDOM FIELDS; RANDOM TOUGHNESS; SELF-CONSISTENT SCHEME; SEMI INFINITES; STANDARD DEVIATIONS; SYSTEM SIZES; TWO REGIMES; WEAK PINNING;

BRITTLE FRACTURE;

EID: 60849130422     PISSN: 03769429     EISSN: 15732673     Source Type: Journal    
DOI: 10.1007/s10704-008-9271-x     Document Type: Article

References (22)

1. Bonamy D, Ponson L, Prades S, Bouchaud E, Guillot C (2006) Scaling exponents for fracture surfaces in homogeneous glass and glassy ceramics. Phys Rev Lett 97(13): 135504
2. Bornert M, Bretheau T, Gilormini P (eds) (2008) Homogenization in mechanics of materials. Lavoisier, Paris (France)
3. Bouchaud JP, Bouchaud E, Lapasset G, Planes J (1993) Models of fractal cracks. Phys Rev Lett 71(14): 2240-2243
4. Charles Y, Vandembroucq D, Hild F, Roux S (2004) Material-independent crack arrest statistics. J Mech Phys Sol 52(7): 1651-1669
5. Charles Y, Vandembroucq D, Hild F, Roux S (2006) Materials-independent crack arrest statistics: Application to indentation experiments. Int J Fract 142(1-2): 51-67
6. Delaplace A, Schmittbuhl J, Måløy KJ (1999) High resolution description of a crack front in a heterogeneous Plexiglas block. Phys Rev E 60(2): 1337-1343
7. Ertas D, Kardar M (1994) Anisotropic scaling in depinning of a flux line. Phys Rev Lett 73(12): 1703-1706
8. Fisher DS (1985) Sliding charge-density waves as a dynamic critical phenomenon. Phys Rev B 31(3): 1396-1427
9. Gao H, Rice JR (1989) First-order perturbation analysis of crack trapping by arrays of obstacles. ASME J Appl Mech 56: 828-836
10. Hansen A, Hinrichsen EL, Roux S (1991) Scale-invariant disorder in fracture and related breakdown phenomena. Phys Rev B 43: 665-678
11. Hill R (1965) A self-consistent mechanics of composite materials. J Mech Phys Solids 13: 213-222
12. Kardar M, Parisi G, Zhang YC (1986) Dynamic scaling of growing interfaces. Phys Rev Lett 56(9): 889-892
13. Lawn BR (1993) Fracture of brittle solids. Cambridge University Press, Cambridge (UK)
14. Morrissey JW, Rice JR (2000) Perturbative simulations of crack front waves. J Mech Phys Solids 48(6-7): 1229-1251
15. Perrin G, Rice JR (1994) Disordering of a dynamic planar crack front in a model elastic medium of randomly variable toughness. J Mech Phys Sol 42(6): 1047-1064
16. Ramanathan S, Fisher DS (1998) Onset of propagation of planar cracks in heterogeneous media. Phys Rev B 58(10): 6026-6046
17. Roux S, Vandembroucq D, Hild F (2003) Effective toughness of heterogeneous brittle materials. Eur J Mech A/Solids 22: 743-749
18. Sanchez-Palencia, E, Zaoui, A (eds) (1987) Homogenization techniques for composite media, Lecture Notes in Physics, vol 272. Springer, Berlin (Germany)
19. Schmittbuhl J, Mäløy KJ (1997) Direct observation of a self-affine crack propagation. Phys Rev Lett 78(20): 3888-3891
20. Schmittbuhl J, Roux S, Vilotte JP, Måløy KJ (1995) Interfacial crack pinning: Effect of nonlocal interactions. Phys Rev Lett 74(10): 1787-1790
21. Tanguy A, Gounelle M, Roux S (1998) From individual to collective pinning: Effect of long-range elastic interactions. Phys Rev E 58(2): 1577-1590
22. Vandembroucq D, Skoe R, Roux S (2004) Universal depinning force fluctuations of an elastic line: Application to finite temperature behavior. Phys Rev E 70(5): 051101