Contact Mechanics for Randomly Rough Surfaces: On the Validity of the Method of Reduction of Dimensionality

Persson, B. N. J.

doi:10.1007/s11249-015-0498-1

Cited by 11 publications

(4 citation statements)

References 28 publications

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“…It should be mentioned that even reliable wear calculations ( Dimaki et al, 2015; as well as calculations of torsional contacts ( Willert, Heß, & Popov, 2015 ) can be done by MDR. We would like to point out, that the applicability of MDR to contact problems between randomly rough surfaces is controversially discussed ( Persson, 2015;. However, its applicability to the solution of axisymmetric contact problems with a simply-connected contact area is no question and the associated field of application is large.…”

Section: The Methods Of Dimensionality Reductionmentioning

confidence: 99%

A simple method for solving adhesive and non-adhesive axisymmetric contact problems of elastically graded materials

Heß

2016

International Journal of Engineering Science

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Section: The Methods Of Dimensionality Reductionmentioning

confidence: 99%

A simple method for solving adhesive and non-adhesive axisymmetric contact problems of elastically graded materials

Heß

2016

International Journal of Engineering Science

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“…So far, the validity of the MDR is reduced to the question of the validity of the original theories of elastic local contact. It should be emphasized that the comment 12 (see also [13][14][15][16] ]), in fact, addresses the validity of the MDR-based model of contact of elastic bodies with rough surfaces. Since the latter problem is intrinsically three dimensional, the mapping rules established in the axisymmetric case may not be applied, and the MDR approach (as it has been developed in Popov and Heß 7 ) to the problem of rough contact uses profound ideas lying at the root of the MDR methodology.…”

Section: Mdr-based Model Of Normal Contact For Rough Surfacesmentioning

confidence: 99%

“…The matter is even worse in the MDR-based 1D contact model for rough contact, where the interpretation of the discrete 1D contact zone is still an open question. In particular, the previously suggested approximate inverse mapping for the area of contact lacks accuracy in the case of saturated contact close to the full contact situation (see the discussion in the literatures [12][13][14][15][16] ). However, the circumstance that the accuracy of this particular approximate inverse mapping rule for the contact area drastically decreases with increasing size of the contact zone should not compromise the whole MDR, and it only means that a new more sophisticated inverse mapping rule is needed for the contact area interpretation.…”

Section: Limitations Of the Mdrmentioning

confidence: 99%

A discussion of the method of dimensionality reduction

Argatov

2015

Proceedings of the Institution of Mechanical Engineers, Part C:

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The Method of Dimensionality Reduction (MDR) can be regarded as a formalism for analytical solution of some commonly encountered classes of contact problems using a “mechanical intuition” based on the Winkler foundation model. Such an approach makes it much easier to account for a wide range of physical effects associated with contact interaction (e.g. friction, adhesion, and damping). However, there is still a controversy about the method and its applications (see, e.g., the comment on validity of the MDR-based model of rough contact) – which we believe comes from a misunderstanding of the method itself, and which, in turn, can be reconsidered in view of the recently published book on the MDR. The MDR was originally introduced for Hertz’s problem of axisymmetric frictionless local contact and was generalized subsequently for arbitrary axisymmetric geometry of linearly elastic bodies in unilateral local contact. The latter problem, for which the MDR yields the exact analytical solution, can be viewed as a base case that is used to extend, in a unified manner, the model of local contact by taking into account adhesion, friction, and viscous damping. In what follows, we overview the main concepts of the method starting with the base-case contact problem in which the MDR is rooted, and discuss limitations of the MDR as well. For the sake of their completeness, some criticisms that apply equally to conventional contact mechanics solutions are also considered. It is emphasized that the axisymmetric Hertz-type contact problems with a circular contact area constitute the proven range of validity of the MDR, while the extension of the method to other types of contact (e.g. axisymmetric with a multiply-connected contact area, non-axisymmetric) is a field ripe for research.

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“…The functional characteristics of nature and industrial surfaces are closely related to their roughness, such as contact mechanics, 1,2 wettability, 3 friction, 4 and sealing. 5 Surface roughness determines the interface stiffness, actual contact area, and void morphology of the contact interface.…”

Section: Introductionmentioning

confidence: 99%

Effect of surface roughness topography on percolation characteristic of contact interface

Zhang

Liu

Zhang

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part J:

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The contact geometry of rough surfaces markedly affects the functional properties such as sealing and lubrication. The effect of surface roughness on the percolation characteristic of elastic contact was studied. The elastic contact of randomly rough surfaces with a glass plate was performed using four different surface roughnesses of silicone rubber blocks as specimens. The results illustrate that the percolation threshold was significantly affected by the valley morphology of a surface. The increase in depth and void volume of valleys improved the connectivity between valleys, but impeded the coalescence of contact clusters, resulting in the extinction of the spanning void cluster allowing fluid flow when the relative contact area was large. Furthermore, the critical pressure and connectivity at the percolation threshold were related to the maximum peak height and autocorrelation length of a surface, respectively.

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Contact Mechanics for Randomly Rough Surfaces: On the Validity of the Method of Reduction of Dimensionality

Cited by 11 publications

References 28 publications

A simple method for solving adhesive and non-adhesive axisymmetric contact problems of elastically graded materials

A simple method for solving adhesive and non-adhesive axisymmetric contact problems of elastically graded materials

A discussion of the method of dimensionality reduction

Effect of surface roughness topography on percolation characteristic of contact interface

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