The autocorrelation function for island areas on self-affine surfaces

Ramisetti, Srinivasa Babu; Campañá, Carlos; Anciaux, Guillaume; Molinari, Jean‐François; Müser, Martin H.; Robbins, Mark O.

doi:10.1088/0953-8984/23/21/215004

Cited by 27 publications

(26 citation statements)

References 31 publications

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“…Self-affine rough surfaces with the desired Hurst exponent H, h′ rms , λ s , and λ L are generated using a Fourier-filtering algorithm described previously (44). Fourier components for each wavevector q → have a random phase and a normally distributed amplitude that depends on the magnitude q.…”

Section: Methodsmentioning

confidence: 99%

Contact between rough surfaces and a criterion for macroscopic adhesion

Pastewka

Robbins

2014

Proc. Natl. Acad. Sci. U.S.A.

275

238

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At the molecular scale, there are strong attractive interactions between surfaces, yet few macroscopic surfaces are sticky. Extensive simulations of contact by adhesive surfaces with roughness on nanometer to micrometer scales are used to determine how roughness reduces the area where atoms contact and thus weakens adhesion. The material properties, adhesive strength, and roughness parameters are varied by orders of magnitude. In all cases, the area of atomic contact is initially proportional to the load. The prefactor rises linearly with adhesive strength for weak attractions. Above a threshold adhesive strength, the prefactor changes sign, the surfaces become sticky, and a finite force is required to separate them. A parameter-free analytic theory is presented that describes changes in these numerical results over up to five orders of magnitude in load. It relates the threshold adhesive strength to roughness and material properties, explaining why most macroscopic surfaces do not stick. The numerical results are qualitatively and quantitatively inconsistent with classical theories based on the Greenwood−Williamson approach that neglect the range of adhesion and do not include asperity interactions.surface roughness | contact mechanics S urfaces are adhesive or "sticky" if breaking contact requires a finite force. At the atomic scale, surfaces are pulled together by van der Waals interactions that produce forces per unit area that are orders of magnitude larger than atmospheric pressure (1). This leads to strong adhesion of small objects, such as Gecko setae (2, 3) [capillary forces may also contribute to Gecko adhesion in humid environments (4, 5)] and engineered mimics (6), and unwanted adhesion is the main failure mechanism in microelectromechanical systems with moving parts (7). Although tape and gecko feet maintain this strong adhesion at macroscopic scales, few of the objects we encounter are sticky. Indeed, our world would come to a halt if macroscopic objects adhered with an average pressure equal to that from van der Waals interactions.The discrepancy between atomic and macroscopic forces has been dubbed the adhesion paradox (8). Experiments show that a key factor underlying this paradox is surface roughness, which reduces the fraction of surface atoms that are close enough to adhere (8-11). Quantitative calculations of this reduction are extremely challenging because of the complex topography of typical surfaces, which have bumps on top of bumps on a wide range of scales (12, 13). In many cases, they can be described as self-affine fractals from a lower wavelength λ s of order nanometers to an upper wavelength λ L in the micrometer to millimeter range (10,14).The traditional Greenwood−Williamson (GW) (15) approach for calculating nonadhesive contact of rough surfaces approximates their complex topography by a set of spherical asperities of radius R. The distribution of asperity heights is assumed to be either exponential or Gaussian, and the long-range elastic interactions between different asperities...

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Section: Methodsmentioning

confidence: 99%

Contact between rough surfaces and a criterion for macroscopic adhesion

Pastewka

Robbins

2014

Proc. Natl. Acad. Sci. U.S.A.

275

238

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“…For most of these phenomena it is critical to accurately estimate the true contact area for given thermo-electro-mechanical loads and given roughness of contacting surfaces. It is now well known that a simple load bearing area model, relying on a geometrical overlap of two rough surfaces considerably overestimates the true contact area [46,60], and for equal contact areas, the former results in a much higher transmissivity in transport problems [15]. Existing analytical models, asperity-based [27,9,66,38,26,1], as well as Persson's model [50,52] with its adjusted version [49], rely on a few approximations and thus cannot provide very accurate results in terms of true contact area over a wide interval of loading conditions (for a detailed discussion and comparison see [37,12,44,73,75]).…”

Section: Introductionmentioning

confidence: 99%

On the accurate computation of the true contact-area in mechanical contact of random rough surfaces

Yastrebov

Anciaux

Molinari

2017

Tribology International

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Abstract.We introduce a corrective function to compensate errors in contact area computations coming from mesh discretization. The correction is based on geometrical arguments and requires only one additional quantity to be computed: the length of contact/non-contact interfaces. The new technique enables us to evaluate accurately the true contact area using a coarse mesh for which the shortest wavelength in the surface spectrum reaches the grid size. The validity of the approach is demonstrated for surfaces with different fractal dimensions and different spectral content using a properly designed mesh convergence test. In addition, we use a topology preserving smoothing technique to adjust the morphology of contact clusters obtained with a coarse grid.

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“…In Ref. [5,6] it was also shown that the contact stress-stress correlation function (in wavevector space) ⟨σ(q)σ(−q)⟩ ∼ q −α , where in the overlap model α = 2+H (where H is the Hurst exponent), while including the long-range elastic coupling α = 1 + H.…”

Section: Introductionmentioning

confidence: 99%

On the Validity of the Method of Reduction of Dimensionality: Area of Contact, Average Interfacial Separation and Contact Stiffness

2013

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It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one dimensional (1D) elastic foundation model. Using this 1D mapping we calculate the contact area and the average interfacial separation between elastic solids with nominally flat but randomly rough surfaces. We show, by comparison to exact numerical results, that the 1D mapping method fails even qualitatively. We also calculate the normal interfacial stiffness K and compare it with the result of an analytical study. We attribute the failure of the elastic foundation model to the neglect of the long-range elastic coupling between the asperity contact regions.

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The autocorrelation function for island areas on self-affine surfaces

Cited by 27 publications

References 31 publications

Contact between rough surfaces and a criterion for macroscopic adhesion

Contact between rough surfaces and a criterion for macroscopic adhesion

On the accurate computation of the true contact-area in mechanical contact of random rough surfaces

On the Validity of the Method of Reduction of Dimensionality: Area of Contact, Average Interfacial Separation and Contact Stiffness

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