1997
DOI: 10.1016/s0022-5096(96)00080-4
|View full text |Cite
|
Sign up to set email alerts
|

Some fractal models of fracture

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

2
73
0

Year Published

2001
2001
2021
2021

Publication Types

Select...
4
4

Relationship

0
8

Authors

Journals

citations
Cited by 144 publications
(75 citation statements)
references
References 36 publications
2
73
0
Order By: Relevance
“…Different formulations based on fractal concepts have been proposed (e.g. Balankin, 1997, Borodich, 1997, Carpinteri and Chiaia, 1996, Carpinteri and Puzzi, 2009, Weiss, 4 2001); specific applications include concrete (Carpinteri and Chiaia, 1995) and particlereinforced composites (Carpinteri and Paggi, 2009), but not FRPs. Bažant (1997) and Bažant and Yavari (2005) have criticised some of the mathematical abstractions in the fractal formalism.…”
Section: MMmentioning
confidence: 99%
“…Different formulations based on fractal concepts have been proposed (e.g. Balankin, 1997, Borodich, 1997, Carpinteri and Chiaia, 1996, Carpinteri and Puzzi, 2009, Weiss, 4 2001); specific applications include concrete (Carpinteri and Chiaia, 1995) and particlereinforced composites (Carpinteri and Paggi, 2009), but not FRPs. Bažant (1997) and Bažant and Yavari (2005) have criticised some of the mathematical abstractions in the fractal formalism.…”
Section: MMmentioning
confidence: 99%
“…(2.5) that, unlike the fractal fracture energy (Borodich, 1992(Borodich, , 1997(Borodich, , 1999Bažant, , 1997aCarpinteri, 1994;Carpinteri and Ferro, 1994;Carpinteri et al, 2002), the ubiquitiformal fracture energy G uf can be obtained directly from physical and geometrical properties of the object under consideration, and then such a ubiquitiformal fracture energy can be taken as a reasonable material parameter, as was proposed by Addison (2000). However, on the one hand, Addison (2000) reached this conclusion via the concept of a pre-fractal, which implied that the fracture surface was of fractal, i.e.…”
Section: Ubiquitiformal Fracture Energy Of Concretementioning
confidence: 99%
“…That is to say, the integral dimensional measures or, intuitively, the area of all the fractal fracture surfaces tend in general to infinity, which makes all the traditional fracture energy vanishing. In fact, over the past decades, to overcome such a difficulty and well describe fractal characteristics of a fractal crack as a direct extension of the concept of traditional fracture energy, some new density kinds of fractal fracture energy parameters defined on a unit fractal measure were proposed, such as the specific energy-absorbing capacity of unit fractal measure (Borodich, 1992(Borodich, , 1997(Borodich, , 1999, fractal fracture energy (Bažant, , 1997a as well as the renormalized fractal fracture energy (Carpinteri, 1994;Carpinteri and Ferro, 1994;Carpinteri et al, 2002), which have been used widely in practical applications. However, as was pointed out recently by Ou et al (2014), such a concept of the fractal fracture energy seems now to be a little questionable, because these fractal fracture energies are both difficult to be determined in practice and lack unambiguous physical meanings (Bažant and Yavari, 2005).…”
Section: Introductionmentioning
confidence: 99%
“…It is well known from experimental observations that cracks and fracture surfaces are statistical fractal objects [7,8,9]. In this sense, knowing how to calculate their true lengths and areas allows a more realistic mathematical description of the fracture phenomenon [10].…”
Section: Introductionmentioning
confidence: 99%
“…For this reason, it is reasonable to consider in an explicit manner the fractal properties of fracture surfaces, and many scientists have worked on the characterization of the topography of the fracture surface using the fractal dimension [12,13]. At certain point, it became necessary to include the topology of the fracture surface into the equations of the Classical Fracture Mechanics theory [6,8,14]. This new "Fractal Fracture Mechanics" (FFM) follows the fundamental basis of the Classical Fracture Mechanics, with subtle modifications of its equations and considering the fractal aspects of the fracture surface with analytical expressions [15,16].…”
Section: Introductionmentioning
confidence: 99%