This paper presents a new formulation of the dynamical Coulomb friction problem in finite dimension with discretized time. The novelty of our approach is to capture and treat directly the friction model as a parametric quadratic optimization problem with second-order cone constraints coupled with a fixed point equation. This intrinsic formulation allows a simple existence proof under reasonable...

Traditional analyses of slip at corners of contacts, based on linear elasticity and a Coulomb friction law, are very sensitive to the details of local geometries, owing to the effects of elastic singularities. Following the use of cohesive-zone models to address such issues in mode-II fracture, we present analyses of slip and wear at corners of contacts when a finite interfacial shear strength ...

The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the reliability of this idea. This paper aims to specify the bulk frictional behaviour of snow avalanches by seeking a universal friction law. Sin...

We show that the static friction force which must be overcome to render a sticking contact sliding is reduced if an external torque is also exerted. As a test system we study a planar disk lying on a horizontal flat surface. We perform experiments and compare with analytical results to find that the coupling between static friction force and torque is nontrivial: It is not determined by the Cou...

In this paper we announce some new mathematical results on the stability of quasistatic paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle.A quasi-static path is said to be stable at some value of the load parameter if, for some finite interval of the load parameter thereafter, the dynamic solutions behave continuously wit...

Rowe's stress–dilatancy relation for frictional (cohesion-less) materials has been a cornerstone of soil mechanics. The original derivation of this relationship was based on incorrect energy minimisation considerations, but the relationship was proven later by De Josselin de Jong using friction laws, and has been confirmed by a large body of experimental results. In contrast, the validity of Ro...

A general control scheme to control flexible arms with friction in the joints is proposed in this paper. This scheme presents the advantage of being robust in the sense that it minimizes the effects of the Coulomb friction existing in the motor and the effects of changes in the dynamic friction coefficient. A justification of the robustness properties of the scheme is given in terms of the sens...

It has been shown recently that steady frictional sliding along an interface between dissimilar elastic solids with Coulomb friction acting at the interface is ill-posed for a wide range of material parameters and friction coefficients. The ill-posedness is manifest in the unstable growth of interfacial disturbances of all wavelengths, with growth rate inversely proportional to the wavelength. ...

We investigate the free cooling of inelastic rough spheres in the presence of Coulomb friction. Depending on the coefficients of normal restitution ǫ and Coulomb friction μ, we find qualitatively different asymptotic states. For nearly complete normal restitution (ǫ close to 1) and large μ, friction does not change the cooling properties qualitatively compared to a constant coefficient of tange...

The generation of higher harmonics of the magnetoplasmon frequency which has recently been reported in strongly coupled two-dimensional Yukawa systems is investigated in detail and, in addition, extended to two-dimensional Coulomb systems. We observe higher harmonics over a much larger frequency range than before and compare the theoretical prediction with the simulations. The influence of the ...