Nonlinear analysis of the stick-slip bifurcation in the creep-controlled regime of dry friction

Nonlinear denoising for characterization of solid friction under low confinement pressure

The present work investigates paper-paper friction dynamics by pulling a slider over a substrate. It focuses on the transition between stick-slip and inertial regimes. Although the device is classical, probing solid friction with the fewest contact damage requires that the applied load should be small. This induces noise, mostly impulsive in nature, on the recorded slider motion and force signals. To address the challenging issue of describing the physics of such systems, we promote here the use of nonlinear filtering techniques relying on recent nonsmooth optimization schemes. In contrast to linear filtering, nonlinear filtering captures the slider velocity asymmetry and, thus, the creep motion before sliding. Precise estimates of the stick and slip phase durations can thus be obtained. The transition between the stick-slip and inertial regimes is continuous. Here we propose a criterion based on the probability of the system to be in the stick-slip regime to quantify this transition. A phase diagram is obtained that characterizes the dynamics of this frictional system under low confinement pressure.

Frictional dynamics of viscoelastic solids driven on a rough surface

We study the effect of viscoelastic dynamics on the frictional properties of a (mean-field) spring-block system pulled on a rough surface by an external drive. When the drive moves at constant velocity V, two dynamical regimes are observed: at fast driving, above a critical threshold V(c), the system slides at the drive velocity and displays a friction force with velocity weakening. Below V(c) the steady sliding becomes unstable and a stick-slip regime sets in. In the slide-hold-slide driving protocol, a peak of the friction force appears after the hold time and its amplitude increases with the hold duration. These observations are consistent with the frictional force encoded phenomenologically in the rate-and-state equations. Our model gives a microscopical basis for such macroscopic description.

Kinetics of the coefficient of friction of elastomers

We study theoretically and numerically the kinetics of the coefficient of friction of an elastomer due to abrupt changes of sliding velocity. Numerical simulations reveal the same qualitative behavior which has been observed experimentally on different classes of materials: the coefficient of friction first jumps and then relaxes to a new stationary value. The elastomer is modeled as a simple Kelvin body and the surface as a self-affine fractal with a Hurst exponent in the range from 0 to 1. Parameters of the jump of the coefficient of friction and the relaxation time are determined as functions of material and loading parameters. Depending on velocity and the Hurst exponent, relaxation of friction with characteristic length or characteristic time is observed.

Chaos on the conveyor belt

The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five).

Master equation approach to friction at the mesoscale

At the mesoscale friction occurs through the breaking and formation of local contacts. This is often described by the earthquakelike model which requires numerical studies. We show that this phenomenon can also be described by a master equation, which can be solved analytically in some cases and provides an efficient numerical solution for more general cases. We examine the effect of temperature and aging of the contacts and discuss the statistical properties of the contacts for different situations of friction and their implications, particularly regarding the existence of stick-slip.

Boundary lubrication with a glassy interface

Recently introduced constitutive equations for the rheology of dense, disordered materials are investigated in the context of stick-slip experiments in boundary lubrication. The model is based on a generalization of the shear transformation zone (STZ) theory, in which plastic deformation is represented by a population of mesoscopic regions which may undergo nonaffine deformations in response to stress. The generalization we study phenomenologically incorporates the effects of aging and glassy relaxation. Under experimental conditions associated with typical transitions from stick-slip to steady sliding and stop-start tests, these effects can be dominant, although the full STZ description is necessary to account for more complex, chaotic transitions.

Aging in humid granular media

Aging behavior is an important effect in the friction properties of solid surfaces. In this paper we investigate the temporal evolution of the static properties of a granular medium by studying the aging over time of the maximum stability angle of submillimetric glass beads. We report the effect of several parameters on these aging properties, such as the wear on the beads, the stress during the resting period, and the humidity content of the atmosphere. Aging effects in an ethanol atmosphere are also studied. These experimental results are discussed at the end of the paper.

Transition from stick-slip to smooth sliding: an earthquakelike model

We present a detailed study of an earthquakelike model that exhibits a "transition" from stick-slip motion to smooth sliding at a velocity of the order of those observed in experiments. This contrasts with the many previous microscopic models in which the transition velocity is many orders of magnitude too large. The results show that experimentally observed smooth sliding at the macroscopic scale must correspond to microscopic-scale stick-slip motion.

Friction and noise-induced coherent structures in boundary lubrication

We examine the effect of stick-slip boundary conditions on the friction generated by a molecularly thin layer of a liquid lubricant separating two plates. For one-dimensional compressible flows, noise-induced coherent dissipative structures on a micron scale are generated due to cooperation between the external drive and the thermal noise. As a function of the thermal noise these structures show a peak in their amplitudes similar to stochastic resonance. At low velocities a reduction in friction with increasing thermal noise is observed.

Tuning friction with noise and disorder

We present numerical and experimental evidence which demonstrates that under certain conditions friction can be reduced by spatial disorder and/or thermal noise. We discuss possible mechanisms for this behavior.