Static Friction between Elastic Solids due to Random Asperities

We review in these notes some dynamical properties of interfaces in random media submitted to an external force. We focuss in particular to the response to a very small force (so called creep motion) and discuss various theoretical aspects of this problem. We consider in details in particular the case of a one dimensional interface (domain wall).

We study the roughening of $d$-dimensional directed elastic interfaces subject to quenched random forces. As in the Larkin model, random forces are considered constant in the displacement direction and uncorrelated in the perpendicular direction. The elastic energy density contains an harmonic part, proportional to $(\partial_x u)^2$, and an anharmonic part, proportional to $(\partial_x u)^{2n}$, where $u$ is the displacement field and $n>1$ an integer. By heuristic scaling a...

In this thesis I discuss analytical approaches to disordered systems using field theory. Disordered systems are characterized by a random energy landscape due to heterogeneities, which remains fixed on the time scales of the phenomena considered. I focus specifically on elastic interfaces in random media, such as pinned domain walls in ferromagnets containing defects, fluid contact lines on rough surfaces, etc. The goal is to understand static properties (e.g. the roughness) ...

We propose and analyze a simple variational model for dislocations at semi-coherent interfaces. The energy functional describes the competition between two terms: a surface energy induced by dislocations that compensate the lattice misfit at the interface, and a far field elastic energy, spent to decrease the amount of needed dislocations. We prove that the former scales like the surface area of the interface, the latter like its diameter. The proposed continuum model is de...

We study the sliding of elastic solids in adhesive contact with flat and rough interfaces. We consider the dependence of the sliding friction on the elastic modulus of the solids. For elastically hard solids with planar surfaces with incommensurate surface structures we observe extremely low friction (superlubricity), which very abruptly increases as the elastic modulus decreases. We show that even a relatively small surface roughness may completely kill the superlubricity st...

We have studied the fluctuation (noise) in the position of sliding blocks under constant driving forces on different substrate surfaces. The experimental data are complemented by simulations using a simple spring-block model where the asperity contact regions are modeled by miniblocks connected to the big block by viscoelastic springs. The miniblocks experience forces that fluctuate randomly with the lateral position, simulating the interaction between asperities on the block...

We review the present state of understanding of solid friction at low velocities and for systems with negligibly small wear effects. We first analyze in detail the behavior of friction at interfaces between wacroscopic hard rough solids, whose main dynamical features are well described by the Rice-Ruina rate and state dependent constitutive law. We show that it results from two combined effects : (i) the threshold rheology of nanometer-thick junctions jammed under confineme...

The coefficient of static friction between solids generally depends on the time they have remained in static contact before the measurement. Such frictional aging is at the origin of the difference between static and dynamic friction coefficients, but has remained difficult to understand. It is usually attributed to a slow increase in the area of atomic contact as the interface changes under pressure. This is however very difficult to quantify as surfaces have roughness at al...

I study how the contact area and the work of adhesion, between two elastic solids with randomly rough surfaces, depend on the relative humidity. The surfaces are assumed to be hydrophilic, and capillary bridges form at the interface between the solids. For elastically hard solids with relative smooth surfaces, the area of real contact and therefore also the sliding friction, are maximal when there is just enough liquid to fill out the interfacial space between the solids, whi...

At finite temperature and in presence of disorder, a one-dimensional elastic interface displays different scaling regimes at small and large lengthscales. Using a replica approach and a Gaussian Variational Method (GVM), we explore the consequences of a finite interface width $\xi$ on the small-lengthscale fluctuations. We compute analytically the static roughness $B(r)$ of the interface as a function of the distance $r$ between two points on the interface. We focus on the ca...