Abstract:
We investigate a simple model of dry friction based on extremal dynamics of asperities. At small velocities, correlations develop between the asperities, whose range becomes infinite in the limit of infinitely slow driving, where the system is self-organized critical. This collective phenomenon leads to effective aging of the asperities and results in velocity dependence of the friction force in the form $F\sim 1- \exp(-1/v)$.

Abstract:
Several workers have established that the Larkin domains for two three dimensional nonmetallic elastic solids in contact with each other at a disordered interface are enormously large. This implies that there should be negligible static friction per unit area in the macroscopic solid limit. The present work argues that the fluctuations in the heights of the random asperities at the interface that occur in the Greenwood-Williamson model can account for static friction.

Abstract:
It is shown on the basis of scaling arguments that a disordered interface between two elastic solids will quite generally exhibit static and "dry friction" (i.e., kinetic friction which does not vanish as the sliding velocity approaches zero), because of Tomlinson model instabilities that occur for small length scale asperities. This provides a possible explanation for why static and "dry" friction are virtually always observed, and superlubricity almost never occurs.

Abstract:
A theoretical account is given of the microscopic basis of the rate- and state-dependent friction (RSF) law. The RSF law describes rock friction quantitatively and therefore it is commonly used to model earthquakes and the related phenomena. But the RSF law is rather empirical and the theoretical basis has not been very clear. Here we derive the RSF law starting from constitutive laws for asperities, and give the atomistic expressions for the empirical RSF parameters. In particular, we show that both the length constant and the state variable are given as the 0th weighted power means of the corresponding microscopic quantities: a linear dimension and the contact duration of each asperity. As a result, evolution laws for the state variable can be derived systematically. We demonstrate that the aging and the slip laws can be derived and clarify the approximations behind these two major evolution laws. Additionally, the scaling properties of the length constant are clarified for fractal distribution of asperities.

Abstract:
Molecular dynamics simulations are used to study contact between a rigid, nonadhesive, spherical tip with radius of order 30nm and a flat elastic substrate covered with a fluid monolayer of adsorbed chain molecules. Previous studies of bare surfaces showed that the atomic scale deviations from a sphere that are present on any tip constructed from discrete atoms lead to significant deviations from continuum theory and dramatic variability in friction forces. Introducing an adsorbed monolayer leads to larger deviations from continuum theory, but decreases the variations between tips with different atomic structure. Although the film is fluid, it remains in the contact and behaves qualitatively like a thin elastic coating except for certain tips at high loads. Measures of the contact area based on the moments or outer limits of the pressure distribution and on counting contacting atoms are compared. The number of tip atoms making contact in a time interval grows as a power of the interval when the film is present and logarithmically with the interval for bare surfaces. Friction is measured by displacing the tip at a constant velocity or pulling the tip with a spring. Both static and kinetic friction rise linearly with load at small loads. Transitions in the state of the film lead to nonlinear behavior at large loads. The friction is less clearly correlated with contact area than load.

Abstract:
We study rubber sliding friction on hard lubricated surfaces. We show that even if the hard surface appears smooth to the naked eye, it may exhibit short wavelength roughness, which may give the dominant contribution to rubber friction. That is, the observed sliding friction is mainly due to the viscoelastic deformations of the rubber by the substrate surface asperities. The presented results are of great importance for rubber sealing and other rubber applications involving (apparently) smooth surfaces.

Abstract:
Rubber friction on wet rough substrates at low velocities is typically 20-30% smaller than for the corresponding dry surfaces. We show that this cannot be due to hydrodynamics and propose a novel explanation based on a sealing effect exerted by rubber on substrate "pools" filled with water. Water effectively smoothens the substrate, reducing the major friction contribution due to induced viscoelastic deformations of the rubber by surface asperities. The theory is illustrated with applications related to tire-road friction.

Abstract:
We calculate the friction force acting on a hard cylinder or spherical ball rolling on a flat surface of a viscoelastic solid. The rolling friction coefficient depends non-linearly on the normal load and the rolling velocity. For a cylinder rolling on a viscoelastic solid characterized by a single relaxation time Hunter has obtained an exact result for the rolling friction, and our result is in very good agreement with his result for this limiting case. The theoretical results are also in good agreement with experiments of Greenwood and Tabor. We suggest that measurements of rolling friction over a wide range of rolling velocities and temperatures may constitute an useful way to determine the viscoelastic modulus of rubber-like materials.

Abstract:
Sliding friction across a thin soft lubricant film typically occurs by stick-slip, the lubricant fully solidifying at stick, yielding and flowing at slip. The static friction force per unit area preceding slip is known from molecular dynamics (MD) simulations to decrease with increasing contact area. That makes the large-size fate of stick-slip unclear and unknown; its possible vanishing is important as it would herald smooth sliding with a dramatic drop of kinetic friction at large size. Here we formulate a scaling law of the static friction force, which for a soft lubricant is predicted to decrease as f_m + \Delta f /A^gamma for increasing contact area A, with gamma>0. Our main finding is that the value of f_m, controlling the survival of stick-slip at large size, can be evaluated by simulations of comparably small size. MD simulations of soft lubricant sliding are presented, which verify this theory.

Abstract:
While dry Coulombic friction is an elementary topic in any standard introductory course in mechanics, the critical distinction between the kinetic and static friction forces is something that is both hard to teach and to learn. In this paper, I describe a geometric model of static friction that may help introductory students to both understand and apply the Coulomb static friction approximation.