Relation between fractal dimension and roughness index for fractal surfaces

Lung, C.W.; Jiang, Jiefeng; Tian, Enke; Zhang, C. H.

doi:10.1103/physreve.60.5121

Cited by 18 publications

(7 citation statements)

References 12 publications

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“…A strong correlation was observed, and it indicated that the fracture surface of the composites was fractal, and the relationship between the impact strength and fractal dimension of the composites obeyed roughly exponential function [7]. Lung et al have also demonstrated that there is a relation between the roughness and the fractal dimension of the surface [45].…”

Section: Fractal Structurementioning

confidence: 90%

Fractal Geometry and Porosity

Agboola¹,

Onyango²,

Popoola³

et al. 2017

Fractal Analysis - Applications in Physics, Engineering and Technology

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A fractal is an object or a structure that is self-similar in all length scales. Fractal geometry is an excellent mathematical tool used in the study of irregular geometric objects. The concept of the fractal dimension, D, as a measure of complexity is defined. The concept of fractal geometry is closely linked to scale invariance, and it provides a framework for the analysis of natural phenomena in various scientific and engineering domains. The relevance of the power law scaling relationships is discussed. Fractal characteristics of porous media and the characteristic method of the porous media are also discussed. Different methods of analysis on the permeability of porous media are discussed in this chapter.

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Section: Fractal Structurementioning

confidence: 90%

Fractal Geometry and Porosity

Agboola¹,

Onyango²,

Popoola³

et al. 2017

Fractal Analysis - Applications in Physics, Engineering and Technology

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“…3. Following similar work by Lung et al [41], Koch-type surfaces are iteratively generated as follows: In each iteration, each line segment is divided into three equal segments; the middle segment is replaced by an isosceles triangle with a unit slope α. By increasing the value of α, we increase the roughness and fractality of the surface.…”

Section: Signature Function Of Fractal Koch Surfacesmentioning

confidence: 99%

“…We use a commonly studied fractal surface structure, namely, the triadic Koch surface [39][40][41], to examine the relationship between friction and surface structure. The initial polygon used to generate the Koch surfaces consists of a series of isosceles triangles of base λ and angle α as shown in Fig.…”

Section: Signature Function Of Fractal Koch Surfacesmentioning

confidence: 99%

Static friction between rigid fractal surfaces

et al. 2015

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Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.

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“…Much work has been invested in understanding why fracture surfaces are self affine and why their roughness seems to fall into a small number of distinct universality classes, see [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Much of this work has been focused on the quasi-static fuse model [1] as a paradigm for brittle fracture.…”

mentioning

confidence: 99%

Roughness of Brittle Fractures as a Correlated Percolation Problem

Bakke¹,

Bjelland²,

Ramstad³

et al. 2003

Physica Scripta

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The morphology of brittle fracture surfaces are self affine with roughness exponents that may be classified into a small number of universality classes. We discuss these in light of the recent proposal that the self affinity is a manifestation of the fracture process being a correlated percolation process. We also study numerically with high precision the roughness exponent in the two-dimensional fuse model with disorder both in breaking thresholds and conductances of the fuses. Our results are consistent with the predictions of the correlated percolation theory.

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Relation between fractal dimension and roughness index for fractal surfaces

Abstract: This paper discusses the relation between fractal dimension and roughness index for fractal surfaces of solids. The applicability of the relation to fracture of Mode III+Mode I complex loading is shown. The applicability to other rough surfaces is discussed.

Cited by 18 publications

References 12 publications

Fractal Geometry and Porosity

Fractal Geometry and Porosity

Static friction between rigid fractal surfaces

Roughness of Brittle Fractures as a Correlated Percolation Problem

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