Fracture propagation in brittle granular matter

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 463, Issue 2087, 2007, Pages 3021-3035

  Einav, Itai ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Breakage mechanics; Comminution; Fracture mechanics; Granular matter; Thermomechanics

Indexed keywords

EID: 36349036120     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2007.1898     Document Type: Article

References (25)

1. Aharonov, E. & Sparks, D. 1999 Rigidity phase transition in granular packings. Phys. Rev. E 60, 6890-6896. (doi:10.1103/PhysRevE.60. 6890)
2. Bak, P., Tang, C. & Wiesenfeld, K. 1987 Self-organized criticality: an explanation of 1/f noise. Phys. Rev. Lett. 59, 381-384. (10.1103/PhysRevLett.59.381)
3. Corwin, E. I., Jaeger, H. M. & Nagel, S. R. 2005 Structural signature of jamming in granular media. Nature 435, 1075-1078. (doi:10.1038/nature03698)
4. Einav, I. 2007a Breakage mechanics. Part I - theory. J. Mech. Phys. Solids 55, 1274-1297. (doi:10.1016/j.jmps.2006.11.003)
5. Einav, I. 2007b Breakage mechanics. Part II - modelling granular materials. J. Mech. Phys. Solids 55, 1298-1320. (doi:10.1016/j.jmps.2006.11.004)
6. Gordon, J. E. 1988 The science of structures and materials. New York, NY: Scientific American Library.
7. Griffith, A. A. 1921 The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. A 221, 163-198. (doi:10.1098/rsta.1921.0006)
8. Hardin, B. O. 1985 Crushing of soil particles. J. Geotech. Eng. ASCE 111, 1177-1192.
9. Irwin, G. R. 1957 Analysis of stresses and strain near the end of a crack traversing a plate. Trans. ASME Ser. E: J. Appl. Mech. 24, 361-364.
10. [Discussion in J. Appl. Mech. 1958 25, 299-303.]
11. Kendall, K. 1978 The impossibility of comminuting small particles by compression. Nature 272, 710-711. (doi:10.1038/272710a0)
12. Kick, F. 1883 Contribution to the knowledge of brittle materials. Dinglers J. 247, 1-5.
13. Lynch, A. J. 1977 Mineral crushing and grinding circuits. Their simulation, optimisation, design and control. Amsterdam, The Netherlands: Elsevier Scientific Publishing Company.
14. McDowell, G. R., Bolton, M. D. & Robertson, D. 1996 The fractal crushing of granular materials. J. Mech. Phys. Solids 44, 2079-2102. (doi:10.1016/S0022-5096(96)00058-0)
15. Nakata, Y., Hyodo, M., Hyde, A. F. L., Kato, Y. & Murata, H. 2001 Microscopic particle crushing of sand subjected to high pressure one-dimensional compression. Soils Found. 41, 69-82.
16. Papamichos, E., Vardoulakis, I. & Ouadfel, H. 1993 Permeability reduction due to grain crushing around a perforation. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 30, 1223-1229. (doi:10.1016/0148-9062(93)90099- Y)
17. Pestana, J. M. & Whittle, A. J. 1995 Compression model for cohesionless solids. Géotechnique 45, 611-631.
18. Rice, J. R. 1978 Thermodynamics of the quasi-static growth of Griffith cracks. J. Mech. Phys. Solids 26, 61-138. (doi:10.1016/0022- 5096(78)90014-5)
19. Roscoe, K. H. & Burland, J. B. 1968 In Engineering plasticity (eds J. Heyman & F. A. Leckie), pp. 535-609. Cambridge, UK: Cambridge University Press.
20. Sammis, C. G., King, G. & Biegel, R. 1987 The kinematics of gouge deformations. Pure Appl. Geophys. 125, 777-812. (doi:10.1007/BF00878033)
21. Schofield, A. N. & Wroth, C. P. 1968 Critical state soil mechanics. London, UK: McGraw-Hill.
22. Turcotte, D. L. 1986 Fractals and fragmentation. J. Geophys. Res. 91, 1921-1926.
23. von Rittinger, R. P. 1867 Textbook of mineral dressing. Berlin, Germany: Ernest and Korn.
24. Walton, K. 1987 The effective elastic moduli of a random packing of spheres. J. Mech. Phys. Solids 35, 213-226. (doi:10.1016/0022- 5096(87)90036-6)
25. Wood, D. M. 2006 Geomaterials with changing grading: a route towards modelling. In Int. Symp. on Geomechanics and Geotechnics of Particulate Media, IS-Yamaguchi, Ube, Japan, 12-14 September 2006, pp. 313-316.