Elastic contact between self-affine surfaces: comparison of numerical stress and contact correlation functions with analytic predictions

By Carlos Campañá, Martin H. Müser, M. Robbins. 2008

134 citations recorded by the source corpus.

Contact between an elastic manifold and a rigid substrate with a self-affine fractal surface is reinvestigated with Green’s function molecular dynamics. The Fourier transforms of the stress and contact autocorrelation functions are found to decrease as |q|−μ where q is the wavevector. Upper and lower bounds on the ratio of the two correlation functions are used to argue that they have the same scaling exponent μ. Analysis of numerical results gives μ = 1+H, where H is the Hurst roughness exponent. This is consistent with Persson’s contact mechanics theory, while asperity models give μ = 2(1+H). The effect of increasing the range of interactions from a hard sphere repulsion to exponential decay is analyzed. Results for exponential interactions are accurately described by recent systematic corrections to Persson’s theory. The relation between the area of simply connected contact patches and the normal force is also studied. Below a threshold size the contact area and force are consistent with Hertzian contact mechanics, while area and force are linearly related in larger contact patches.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/52edd9c9aa089ce78e8f796f4377ff920f2f2fa0

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In Atomic and Molecular Physics, and Optics

In Mechanics of Materials

Citations in the corpus

A new efficient numerical method for contact mechanics of rough surfaces (2012, background): “It is worth noticing that other calculations (Hyun and Robbins, 2007; Hyun et al., 2004; Luan et al., 2006; Campana et al., 2008; Cheng and Robbins, 2010) do not present this trend.”
A Review of Elastic–Plastic Contact Mechanics (2017, background): “After some early turmoil [189,190], in recent years researchers appear to be coming to a consensus of what a valid elastic rough surface contact model looks like and which of those in the literature meet these expectations [191–196] (except perhaps when adhesion is considered [197]).”
Colloquium: Modeling friction: From nanoscale to mesoscale (2011, background): “The effect of elastic interactions due to the contact of self-affine surfaces has been studied analytically and numerically, revealing that the solid indeed deforms elastically due to the contact (Persson, 2006; Campana, Müser, and Robbins, 2008; Campana, Persson, and Müser, 2011).”
Interfacial separation between elastic solids with randomly rough surfaces: Comparison between theory and numerical techniques (2011, background): “Here, the long range elastic coupling between the asperity contact regions, which is neglected in the GW model, is now known to strongly influence contact mechanics (Persson, 2008; Campañá et al., 2008). If an asperity is pushed downwards at a certain location, the elastic deformation field extends ”
Meeting the Contact-Mechanics Challenge (2017, background): “localized and therefore too large compared to full solutions that include long-range elasticity [16].”