Morphological fractal dimension versus power-law exponent in the scaling of damaged media

International Journal of Damage Mechanics

Volumn 18, Issue 3, 2009, Pages 259-282

  Carpinteri, Alberto ^a   Lacidogna, Giuseppe ^a   Niccolini, Gianni ^a   Puzzi, Simone ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Acoustic emission; Concrete structures; Crack size distribution; Damage mechanics; Fractal dimension

Indexed keywords

3-D PROBLEMS; AE SIGNALS; B VALUES; BARYCENTERS; CONCRETE SPECIMENS; CONCRETE STRUCTURES; CRACK LENGTHS; CRACK NETWORKS; CRACK SIZE DISTRIBUTION; DAMAGE MECHANICS; DAMAGE PROCESS; DAMAGED MATERIALS; FRACTAL GEOMETRIES; FRACTURE PROCESS; FRACTURE SURFACES; FRACTURE SYSTEMS; GROWING CRACKS; LOWER LIMITS; POST-PROCESSING; POWER LAWS; POWER-LAW EXPONENTS; SCIENTIFIC FIELDS; SPATIAL DISTRIBUTIONS; STATISTICAL MODELS; THEORETICAL BASIS; TWO-POINT CORRELATIONS;

ACOUSTIC EMISSION TESTING; ACOUSTIC EMISSIONS; ACOUSTICS; CONCRETES; CRACKS; FRACTURE; MECHANICS; PARTIAL DISCHARGES; POPULATION STATISTICS; SIZE DISTRIBUTION; STATISTICAL TESTS; THREE DIMENSIONAL; VALUE ENGINEERING;

FRACTAL DIMENSION;

EID: 64849112488     PISSN: 10567895     EISSN: 15307921     Source Type: Journal    
DOI: 10.1177/1056789508098700     Document Type: Article

References (38)

1. Aki, K. (1981). A Probabilistic Synthesis of Precursory Phenomena in Earthquake Prediction, In: Simpson, D.W. and Richards, P.G. pp. 566-574, American Geophysical Union, Washington.
2. Bonnet, E., Bour, O., Odling, N.E., Davy, P., Main, I., Cowie, P. and Berkowitz, B. (2001). Scaling of Fracture Systems in Geological Media, Reviews of Geophysics, 3: 347-383.
3. Bour, O. and Davy, P. (1999). Clustering and Size Distributions of Fault Patterns: Theory and Measurements, Geoph. Res. Lett., 13: 2001-2004.
4. Bour, O., Davy, P., Darcel, C. and Odling, N. (2002). A Statistical Scaling Model for Fracture Network Geometry, with Validation on a Multiscale Mapping of a Joint Network (Hornelen Basin, Norway), Journal of Geophysical Research, 107: 2001 JB000176.
5. Caneva, A. and Smirnov, V. (2004). Using the Fractal Dimension of Earthquake Distributions and the Slope of the Recurrence Curve to Forecast Earthquakes in Colombia, Earth Sciences Research Journal, 8: 3-9.
6. Carpinteri, A. (1986). Mechanical Damage and Crack Growth in Concrete: Plastic Collapse to Brittle Fracture, Martinus Nijhoff Publishers, Dordrecht.
7. Carpinteri, A. (1989). Decrease of Apparent Tensile and Bending Strength with Specimen Size: Two Different Explanations Based on Fracture Mechanics, International Journal of Solids and Structures, 25: 407-429.
8. Carpinteri, A. (1994 a). Scaling Laws and Renormalization Groups for Strength and Toughness of Disordered Materials, International Journal of solids and structures, 31: 291-302.
9. Carpinteri, A. (1994 b). Fractal Nature of Material Microstructure and Size Effects on Apparent Mechanical Properties, Mechanics of Materials, 18: 89-101.
10. Carpinteri, A. and Pugno, N. (2002). One, Two, and Three-Dimensional Universal Laws for Fragmentation Due to Impact and Explosion, Journal of Applied Mechanics, 69: 854-856.
11. Carpinteri, A., Lacidogna, G. and Pugno, N. (2004). Scaling of Energy Dissipation in Crushing and Fragmentation: A Fractal and Statistical Analysis Based on Particle Size Distribution, International Journal of Fracture, 129: 131-139.
12. Carpinteri, A., Lacidogna, G. and Niccolini, G. (2005). Crack Localisation in a Large-Sized R.C. Beam Through the Acoustic Emission Technique, In: Proc. of the 17th National Congress of Theoretical and Applied Mechanics (AIMETA), Florence, CD-Rom, Paper No. 23.
13. Carpinteri, A., Lacidogna, G. and Niccolini, G. (2006 a). Critical Behaviour in Concrete Structures and Damage Localization by Acoustic Emission, Key Engineering Materials, 312: 305-310.
14. Carpinteri, A., Lacidogna, G. and Pugno, N. (2006 b). Richter's Laws at the Laboratory Scale Interpreted by Acoustic Emission, Magazine of Concrete Research, 58: 619-625.
15. Carpinteri, A., Lacidogna, G. and Niccolini, G. (2007). Critical Defect Size Distributions in Concrete Structures Detected by the Acoustic Emission Technique, Meccanica, 43: 349-363.
16. Colombo, S., Main, I.G. and Forde, M.C. (2003). Assessing Damage of Reinforced Concrete Beam Using "b-value" Analysis of Acoustic Emission Signals, Journal of Materials in Civil Engineering ASCE, 15: 280-286.
17. Davy, P., Sornette, A. and Sornette, D. (1990). Some Consequences of a Proposed Fractal Nature of Continental Faulting, Nature, 348: 56-58.
18. Falconer, K. (1990). Fractal Geometry, J. Wiley & Sons, Chichester.
19. Feder, J. (1988). Fractals, Plenum Press, New York and London.
20. Grassberger, P. and Procaccia, I. (1983). Characterization of Strange Attractors, Phys. Rev. Lett., 50: 346-349.
21. Hausdorff, F. (1919). Dimension und Äusseres Mass, Mathematische Annalen, 79: 157-179.
22. Ju, J.W. and Chen, T.M. (1992). Effective moduli of elastic composites containing microcracks or microvoids, In: D.H. Allen, and D.C. Lagoudas (ed.), Damage Mechanics in Composites, AMD-Vol. 150 and AD-Vol. 32, pp. 181-190, ASME Press, New York, Nov. 1992.
23. King, G. (1986). Speculations on the Geometry of the Initiation and Termination Processes of Earthquake Rupture and its Relation to Morphology and Geological Structure, Pure Appl. Geophys., 124: 567-585.
24. Krajcinovic, D. (1996). Damage Mechanics, Elsevier, Amsterdam.
25. Krajcinovic, D. and Rinaldi, A. (2005). Statistical Damage Mechanics - 1. Theory, Journal of Applied Mechanics, 72: 76-85.
26. Lacidogna, G. and Carpinteri, A. (2006). Monitoring Durability Performances of Concrete and Masonry Structures by Acoustic Emission, Fracture of Nano and Engineering Materials and Structures Proc. of the 16th European Conference of Fracture, Alexandroupolis, Greece, 2006, Ed. E.E. Gdoutos, Springer, Dordrecht, CD-ROM, Paper N. 218.
27. Mandelbrot, B.B. (1982). The Fractal Geometry of Nature, W. H. Freeman, New York.
28. Newman, M.E.J. (2005). Power laws, Pareto distributions and Zipf's law. Contemporary Physics, 46: 323-351.
29. Ohtsu, M. (1996). The History and Development of Acoustic Emission in Concrete Engineering, Magazine of Concrete Research, 48: 321-330.
30. Okubo, P.G. and Aki, K. (1987). Fractal Geometry in the San Andreas Fault System, J. Geophys. Res., 92: 345-355.
31. Rao, M.V.M.S. and Lakshmi, K.J.P. (2005). Analysis of b-value and Improved b-value of Acoustic Emissions Accompanying Rock Fracture, Current Science, 89: 1577-1582.
32. Rinaldi, A., Mastilovic, S. and Krajcinovic, D. (2006). Statistical Damage Mechanics - 2. Constitutive Relations, Journal of Theoretical and Applied Mechanics, 44: 585-602.
33. Sammis, C.G., Osborne, R.H., Anderson, J.L., Banerdt, M. and White, P. (1986). Self-Similar Cataclasis in the Formation of Fault-Gouge, Pure Appl. Geophys, 123: 53-78.
34. Sammis, C.G. and Steacy, S.J. (1995). Fractal Fragmentation in Crustal Shear Zones. In: Barton, C.C. and La Pointe R. (eds), Fractals in the Earth Sciences, Plenum Press, New York, pp. 179-204.
35. Sammonds, P.R., Meredith, P.G., Murrel, S.A.F. and Main, I.G. (1994). Modelling the damage evolution in rock containing porefluid by acoustic emission, Proc. of Eurock'94, Balkema, Rotterdam, The Netherlands.
36. Schorlemmer, D., Wiemer, S. and Wyss, M. (2005). Variations in Earthquake-Size Distribution Across Different Stress Regimes, Nature, 348: 539-542.
37. Turcotte, D.L. (1986). A Fractal Model for Crustal Deformation, Tectonophysics, 132: 261-269.
38. Turcotte, D.L. (1997). Fractals and Chaos in Geology and Geophysics, Cambridge University Press, Cambridge.