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2014 | Vol. 52 nr 1 | 37--46
Tytuł artykułu

Ubiquitiform in applied mechanics

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We demonstrate that a physical object in nature should not be described as a fractal, despite an ideal mathematical object, rather a ubiquitiform (a terminology coined here for a finite order self-similar or self-affine structure). It is shown mathematically that a ubiquitiform must be of integral dimension, and that the Hausdorff dimension of the initial element of a fractal changes abruptly at the point at infinity, which results in divergence of the integral dimensional measure of the fractal and makes the fractal approximation to a ubiquitiform unreasonable. Therefore, instead of the existing fractal theory in applied mechanics, a new type of ubiquitiformal one is needed.
Słowa kluczowe
Wydawca

Rocznik
Strony
37--46
Opis fizyczny
Bibliogr. 48 poz., rys.
Twórcy
autor
  • Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China, zcou@bit.edu.cn
autor
  • Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China
autor
  • Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China
autor
  • Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing, China
Bibliografia
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  • 4. Balankin A.S., 1997, Physics of fracture and mechanics of self-affine cracks, Engineering Fracture Mechanics, 57, 135-203
  • 5. Barenblatt G.I., 1993, Micromechanics of fracture, Theoretical and Applied Mechanics 1992, 25-52
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  • 8. Ba˘zant Z.P., Yavari A., 1997, Scaling of quasibrittle fracture: hypotheses of invasive and lacunar fractality, International Journal of Fracture, 83, 41-65
  • 9. Ba˘zant Z.P., Yavari A., 2005, Is the cause of size effect on structural strength fractal or energeticstatistical? Engineering Fracture Mechanics, 72, 1-31
  • 10. Borodich F.M., 1997, Some fractal models of fracture, Journal of the Mechanics and Physics of Solids, 45, 239-259
  • 11. Borodich F.M., 1999, Fractals and fractal scaling in fracture mechanics, International Journal of Fracture, 95, 239-259
  • 12. Carpinteri A., 1994, Fractal nature of material microstructure and size effects on apparent mechanical properties, Mechanics of Materials, 18, 89-101
  • 13. Carpinteri A., Chiaia B., Cornetti P., 2002, A scale-invariant cohesive crack model for quasibrittle materials, Engineering Fracture Mechanics, 69, 207-217
  • 14. Carpinteri A., Paggi M., 2010, A unified fractal approach for the interpretation of the anomalous scaling laws in fatigue and comparison with existing models, International Journal of Fracture, 161, 41-52
  • 15. Carpinteri A., Puzzi S., 2008, Self-similarity in concrete fracture: size-scale effects and transition between different collapse mechanisms, International Journal of Fracture, 154, 167-175
  • 16. Cherepanov G.P., Balankin A.S., Ivanova, V.S., 1995, Fractal fracture mechanics? A review, Engineering Fracture Mechanics, 51, 997-1033
  • 17. Chudnovsky A., Wu S., 1992, Evaluation of energy release rate in the crack-microcrack interaction problem, International Journal of Solids and Structures, 29, 1699-1709
  • 18. Cotsovos D.M., Pavlović M.N., 2008a, Numerical investigation of concrete subjected to compressive impact loading. Part 1: A fundamental explanation for the apparent strength gain at high loading rates, Computers and Structures, 86, 145-163
  • 19. Cotsovos D.M., Pavlović M.N., 2008b, Numerical investigation of concrete subjected to compressive impact loading. Part 2: Parametric investigation of factors affecting behaviour at high loading rates, Computers and Structures, 86, 164-180
  • 20. Cotsovos D.M., Pavlović M.N., 2008c, Numerical investigation of concrete subjected to high rates of uniaxial tensile loading, International Journal of Impact Engineering, 35, 319-335
  • 21. Davey K., Alonso Rasgado M.T., 2011, Analytical solutions for vibrating fractal composite rods and beams, Applied Mathematical Modelling, 35, 1194-1209
  • 22. Davey K., Prosser R., 2013, Analytical solutions for heat transfer on fractal and pre-fractal domains, Applied Mathematical Modelling, 37, 554-569
  • 23. Edgar G., 2008, Measure, Topology, and Fractal Geometry, Springer, New York
  • 24. Falconer K., 2003, Fractal Geometry, Wiley, Chichester
  • 25. Fleury V., 1997, Branched fractal patterns in non-equilibrium electrochemical deposition from oscillatory nucleation and growth, Nature, 390, 145-148
  • 26. G¨ozen I., Dommersnes P., Czolkos I., Jesorka A., Lobovkina1 T., Orwar1 O., 2010, Fractal avalanche ruptures in biological membranes, Nature Materials, 9, 908-912
  • 27. Krohn C.E., Thompson, A.H., 1986, Fractal sandstone pores: Automated measurements Rusing scanning-electron-microscope images, Physical Review B, 33, 6366-6374
  • 28. Ma D., Stoica A.D., Wang X.L., 2009, Power-law scaling and fractal nature of medium-range order in metallic glasses, Nature Materials, 8, 30-34
  • 29. Mandelbrot B.B., 1967, How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science, 156, 636-638
  • 30. Mandelbrot B.B., 1977, Fractals: Form, Chance, and Dimension, Freeman, San Francisco
  • 31. Mandelbrot B.B., 1982, The Fractal Geometry of Nature, Freeman, New York
  • 32. Mandelbrot B.B., Passoja D.E., Paullay A.J., 1984, Fractal character of fracture surfa ces of metals, Nature, 308, 721-722
  • 33. Martinez-Lopez F., Cabrerizo-Vilchez M.A., Hidalgo-Alvarez R., 2001, An improved method to estimate the fractal dimension of physical fractals based on the Hausdorff definition, Physica A, 298, 387-399
  • 34. Mecholsky J.J., Passoja D.E., Feinberg-Ringle K.S., 1989, Quantitative analysis of brittle fracture surfaces using fractal geometry, Journal of the American Ceramic Society, 72, 60-65
  • 35. Ou Z.C., Duan Z.P., Huang F.L., 2010, Analytical approach to the strain rate effect on the dynamic tensile strength of brittle materials, International Journal of Impact Engineering, 37, 942-945
  • 36. Panagiotopoulos P.D, Panagouli O.K., Koltsakis E.K., 1995, The B.E.M. in plane elastic bodies with cracks and/or boundaries of fractal geometry, Computational Mechanics, 15, 350-363
  • 37. Panagiotopoulos P.D, Panagouli O.K., Mistakidis E.S., 1993, Fractal geometry and fractal material behavior in solids and structures, Archive of Applied Mechanics, 63, 1-24
  • 38. Pande C.S., Richards L.R., Smith S., 1987, Fractal characteristics of fractured surfaces, Journal of Materials Science Letters, 6, 295-297
  • 39. Pugno N.M., Ruoff R.S., 2004, Quantized fracture mechanics, Philisophical Magazine, 84, 2829-2845
  • 40. Ray K.K., Mandal G., 1992, Study of correlation between fractal dimension and impact energy in a high strength low alloy steel, Acta Metallurgica et Materialia, 40, 463-469
  • 41. Saouma V.E., Barton C.C., 1994, Fractals, Fractures, and size effects in concrete, Journal of Engineering Mechanics, 120, 835-854
  • 42. Saouma V.E., Barton C.C., Gamaleldin, N.A., 1990, Fractal characterization of fracture surfaces in concrete, Engineering Fracture Mechanics, 35, 47-53
  • 43. Taylor D., 2004, Predicting the fracture strength of ceramic materials using the theory of critical distances, Engineering Fracture Mechanics, 71, 2407-2416
  • 44. Taylor D., 2007, The Theory of Critical Distances, Elsevier, Oxford
  • 45. Taylor D., 2008, The theory of critical distances, Engineering Fracture Mechanics, 75, 1696-1705
  • 46. Turcotte D.L., 1997, Fractals and Chaos in Geology and Geophysics, Cambridge, New York
  • 47. Wnuk M.P., Yavari A., 2005, A correspondence principle for fractal and classical cracks, Engineering Fracture Mechanics, 72, 2744-2757
  • 48. Xie H.P., Sanderson D.J., 1995, Fractal kinematics of crack propagation in geomaterials, Engineering Fracture Mechanics, 50, 529-536
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.baztech-4390df99-fda3-4cac-8745-5e2f5560e307
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