Multifractal scaling laws in the breaking behaviour of disordered materials

Chaos, Solitons and Fractals

Volumn 8, Issue 2 SPEC. ISS., 1997, Pages 135-150

  Carpinteri, Alberto ^a   Chiaia, Bernardino ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000111514     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0960-0779(96)00088-4     Document Type: Article

References (26)

1. A. Carpinteri and B. Chiaia, Power scaling laws and dimensional transitions in solid mechanics. Chaos, Solitons & Fractals 7, 1343-1364 (1996).
2. M. S. El Naschie, Kolmogorov turbulence, Apollonian fractals and the Cantorian model of quantum space-time. Chaos, Solitons & Fractals 7, 147-149 (1996).
3. A. Carpinteri and B. Chiaia, Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy. Mater. Struct. 28, 435-443 (1995).
4. V. E. Saouma, Fractals, fractures, and size effects in concrete. J. Engng Mech. 120, 835-854 (1993).
5. M. A. Issa and A. M. Hammad, Fractal characterization of fracture surfaces in mortar. Cem. Concr. Res. 23, 7-12 (1993).
6. B. B. Mandelbrot, D. E. Passoja and A. J. Paullay, Fractal character of fracture surfaces of metals. Nature 308, 721-722 (1984).
7. S. R. Brown, A note on the description of surface roughness using fractal dimension, Geophys. Res. Lett. 14, 1095-1098 (1987).
8. G. I. Barenblatt and L. R. Botvina, Self-similarity of fatigue fracture, Defect accumulation. Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela 4, 161-165 (1983).
9. A. Bunde and S. Havlin, Fractals and Disordered Systems. Springer, Berlin (1991).
10. A. Carpinteri, Fractal nature of material microstructure and size effects on apparent mechanical properties. Mech. Mater. 18, 89-101 (1994).
11. C. A. Rogers, Hausdorff Measure. Cambridge University Press, Cambridge (1970).
12. G. I. Barenblatt, Intermediate asymptotics, scaling laws and renormalization group in continuum mechanics. Meccanica 28, 177-184 (1993).
13. A. Carpinteri, Mechanical Damage and Crack Growth in Concrete: Plastic Collapse to Brittle Fracture. Martinus Nijhoff Publishers, Dordrecht (1986).
14. K. G. Wilson, Renormalization group and critical phenomena. Phys. Rev. B 4, 3174-3205 (1971).
15. RILEM Technical Committee 50, Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams. Draft Recommendation. Mater. Struct. 18, 287-290 (1985).
16. B. B. Mandelbrot, Self-affine fractals and fractal dimension. Phys. Scr. 32, 257-260 (1985).
17. A. Chudnowski and B. Kunin, A probabilistic model of brittle crack formation. J. Appl. Phys. 62, 4124-4133 (1987).
18. A. Carpinteri and B. Chiaia, Size effects on concrete fracture energy: Dimensional transition from order to disorder. Mater. Struct. 29, 259-266 (1996).
19. A. Carpinteri, B. Chiaia and G. Ferro, Size effects on nominal tensile strength of concrete structures: Multifractality of material ligaments and dimensional transition from order to disorder. Mater. Struct. 28, 311-317 (1995).
20. A. Carpinteri, Scaling laws and renormalization groups for strength and toughness of disordered materials. Int. J. Solids Struct. 31, 291-302 (1994).
21. L. Nottale, Scale relativity, fractal space-time and quantum mechanics. Chaos, Solitons & Fractals 4, 316-389 (1994).
22. A. Carpinteri, B. Chiaia and G. Ferro, An extensive application to nominal strength size effect of concrete structures. Report 51, Dept. Struct. Eng. Politech. Turin, Torino (1995).
23. Z. P. Bazant, Size effect in blunt fracture: concrete, rock, metal. J. Eng. Mech. 110, 518-535 (1984).
24. M. Elices, G. V. Guinea and J. Planas, Measurement of the fracture energy using three-point bend tests: Part 3 - Influence of cutting the P-δ tail. Mater. Struct. 25, 327-334 (1992).
25. P. C. Perdikaris and A. Romeo, Effect of size and compressive strength on the fracture energy of plain concrete. In Proceedings of the First International Conference on Fracture Mechanics of Concrete Structures, FRAMCOS, edited by Z. P. Bazant, Breckenridge, USA, pp. 550-555 (1992).
26. T. Hasegawa, T. Shioya and T. Okada, Size effect on splitting tensile strength of concrete, Proceedings of the 7th Conference of the Japan Concrete Institute, JCI, pp. 309-312 (1985).