The present paper is concerned with the unilateral contact model and the Coulomb friction law in linear elastostatics. We consider a mixed formulation in which the unknowns are the displacement field and the normal and tangential constraints on the contact area. The chosen finite element method involves continuous elements of degree one and continuous piecewise affine multipliers on the contact...

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...

This paper presents the finite element analysis to study the stress distribution of nickel based superalloy HASTELLOY C-2000 in end milling operation. A commercial finite element software was used to develop modeling and analysis the distribution of stress components in the machined surface after end milling of HASTELLOY C-22HS using coated carbide tools. The friction interaction along the tool...

For a point mass subject to Coulomb friction in feedback with a PID controller, we consider a model based on a differential inclusion comprising all the possible magnitudes of static friction during the stick phase and having unique solutions. We study the set of all equilibria and we establish its global asymptotic stability using a discontinuous Lyapunovlike function, and a suitable LaSalle’s...

Friction is a classical field that goes back to Leonardo da Vinci, Guilliame Amonton, and Charles Augustin de Coulomb. Amonton found that friction force is proportional to normal load, but surprisingly is independent of the area of the apparent contact surface. This observation is known as the Amonton’s paradox. The apparent contact surface is the geometric object surface projected to the conta...

where h is the avalanche thickness, Q is the depth averaged downslope volume flux and x is the curvilinear downslope coordinate. The source term s on the right-hand side of (2) is composed of the downslope component of gravitational acceleration, the Coulomb sliding friction with basal angle of friction δ and gradients of the basal topography height, b, above the curvilinear coordinate system. ...

This study introduces two types of self-oscillating circuits that are frequently found in power electronics applications. Special effort is made to relate the circuits to the analogous mechanical systems of some important scientific inventions: Galileo’s pendulum clock and Coulomb’s friction model. A little touch of related history and philosophy of science will hopefully encourage curiosity, a...

The change of the friction law from a mesoscopic level to a macroscopic level is studied in the spring-block models introduced by Burridge-Knopoff. We find that the Coulomb law is always scale invariant. Other proposed scaling laws are only invariant under certain conditions.

This note presents an extension of the absolute stability problem and of the Lagrange–Dirichlet theorem, when the nonlinearities entering the model are considered within the class of monotone multivalued mappings (consequently including operators with piecewise-linear graphs that may represent physical e3ects like Coulomb friction, dead-zones, saturations, elasto-plasticity, and unilateral cons...

In a recent paper [2], we prove an abstract existence result for the Coulomb friction problem in discrete time. This problem must be solved at each time step when performing a simulation of the dynamics of a mechanical system involving unilateral contact and Coulomb friction (expressed here at the level of velocities). In this paper, we only recall this result and the gist of its proof and then...