Scaling of geological discontinuity normal load–deformation response using fractal geometry

Plesha, Michael E.; Ni, Demai

doi:10.1002/nag.149

Cited by 14 publications

(4 citation statements)

References 19 publications

(25 reference statements)

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“…Then mushroom-like structures [1], and various hierarchical (one-level and multi-level) structures were proposed [49,53,54]. It is interesting to mention that the idea of hierarchical one-level and multi-level structures was initially developed in application to the modelling of surface roughness [55][56][57]. Here, two prototypes of non-axisymmetric elements of artificial adhesive structures have been considered in detail.…”

Section: Discussionmentioning

confidence: 99%

Interaction of a non-axisymmetric artificial single spatula with rough surfaces

Cheng,

Jiang,

Borodich

et al. 2024

Interface Focus.

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Hair-like attachment structures are frequently used by animals to create stable contact with rough surfaces. Previous studies focused primarily on axisymmetric biomimetic models of artificial spatulas, such as those with a mushroom-shaped and cylinder-shaped geometry, in order to simulate the so-called gecko effect. Here, two geometric prototypes of artificial adhesive structures with non-axisymmetric properties were designed. The investigation of the prototype’s interactions with rough surfaces was carried out using the finite element software ABAQUS. Under increasing vertical displacement, the effect of asperity size on the contact pressure evolution of the spatula was investigated. It has been demonstrated that the contact behaviour is greatly affected by the flexibility of the spatula, which is caused by its variable thickness. The thinner spatula shows a higher nominal contact area and attaches more strongly to various rough surfaces. Although a thicker spatula is more susceptible to the ‘leverage’ phenomenon, which occurs when excessively applied displacements prematurely reduce the nominal contact area, it obtains the ability to regulate attachment during unidirectional loading. Two non-axisymmetric prototypes provide different design concepts for the artificial adhesives. It is hoped that this study will provide fresh viewpoints and innovations that contribute to the development of biologically inspired adhesives.

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Section: Discussionmentioning

confidence: 99%

Interaction of a non-axisymmetric artificial single spatula with rough surfaces

Cheng,

Jiang,

Borodich

et al. 2024

Interface Focus.

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“…For example, the C B profile introduced by one of the authors (F.B.) [16,18] and some modifications of the profile (see, e.g., [19][20][21]) are single-level models, while the profile introduced by Borodich and Onishchenko [22,23] is a multilevel model.…”

Section: Preliminaries Scales and Levels Of Surface Roughnessmentioning

confidence: 99%

A Multiscale Statistical Analysis of Rough Surfaces and Applications to Tribology

Borodich,

Pepelyshev,

Jin

2024

Mathematics

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Mathematical modelling of surface roughness is of significant interest for a variety of modern applications, including, but not limited to, tribology and optics. The most popular approaches to modelling rough surfaces are reviewed and critically examined. By providing counterexamples, it is shown that approaches based solely on the use of the fractal geometry or power spectral density have many drawbacks. It is recommended to avoid these approaches. It is argued that the surfaces that cannot be distinguished from the original rough surfaces can be synthesised by employing the concept of the representative elementary pattern of roughness (REPR), i.e., the smallest interval (or area) of a rough surface that statistically represents the whole surface. The REPR may be extracted from surface measurement data by the use of the “moving window” technique in combination with the Kolmogorov–Smirnov statistic.

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“…At least two kind of contact problems can be solved for a punch described by the C B profile Mosolov, 1991, 1992). The model was developed further by Borodich and Onishchenko (1993), Warren and Krajcinovic (1996), Plesha and Ni (2001), and others. Although introduced the idea of hierarchical structure of roughness, there were no papers developing the idea of "bump on bump" structure of roughness until Onishchenko (1993, 1999) introduced the multilevel hierarchical model of roughness.…”

Section: Fractals Approaches To Surface Topographymentioning

confidence: 99%

Contact Mechanics Perspective of Tribology

2021

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Scaling of geological discontinuity normal load–deformation response using fractal geometry

Cited by 14 publications

References 19 publications

Interaction of a non-axisymmetric artificial single spatula with rough surfaces

Interaction of a non-axisymmetric artificial single spatula with rough surfaces

A Multiscale Statistical Analysis of Rough Surfaces and Applications to Tribology

Contact Mechanics Perspective of Tribology

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