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1

Friction Between a Body with an Elastic Layer and Vibrating Surface

Majewski T., Saenz J. A., Sokołowska R.

Machine Dynamics Problems

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2006

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Vol. 30, No. 2

103-112

EN

This paper presents the behavior of an object that contacts a vibrating plane through an elastic layer. The Coulomb model of friction is used. The aim of this paper is to show how the vibration and elasticity of the contact zone change the magnitude of the coefficient of friction. Consequently, an equivalent friction coefficient is defined. During the analysis and simulation for different parameters of vibration, the presence of stick-slip phenomenon for a specific range of the pushing force is noted. For some ranges of vibration of the base, dry friction can be presented as an equivalent viscous damping.

2

A Model for Adhesive Frictional Contact

Sofonea M., Lerguet Z.

Machine Dynamics Problems

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2006

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Vol. 30, No. 2

158-168

EN

The aim of this paper is to present a mathematical model which describes the quasistatic process of adhesive frictional contact between a deformable body and an obstacle, the so-called foundation. The material's behavior is assumed to be elastic, with a nonlinear constitutive law; the adhesive contact is modelled with a surface variable, the bonding field, associated to the normal compliance condition and the static version of Coulomb's law of dry friction. We describe the assumptions which lead to the mathematical model of the process and derive a variational formulation of the problem; then, under a smallness assumption on the coefficient of friction, we prove the uniqueness of the solution for the model.

3

A quasistatic contact problem with slip dependent coefficient of friction for elastic materials

Corneschi C., Hoarau-Mantel T.-V. T.-V., Sofonea M.

Journal of Applied Analysis

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2002

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Vol. 8, nr 1

63-82

EN

We consider a mathematical model which describes the frictional contact between a deformable body and an obstacle, say a foundation. The body is assumed to be linear elastic and the contact is modeled with a version of Coulomb's law of dry friction in which the normal stress is prescribed on the contact surface. The novelty consists here in the fact that we consider a slip dependent coefficient of friction and a quasistatic process. We present two alternative yet equivalent formulations of the problem and establish existence and uniqueness results. The proofs are based on a new result obtained in [10] in the study of evolutionary variational inequalities.

4

On Finite Element Uniqueness Studies for Coulomb's Frictional Contact Model

Hild P.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 1

41-50

EN

We are interested in the finite element approximation of Coulomb's frictional unilateral contact problem in linear elasticity. Using a mixed finite element method and an appropriate regularization, it becomes possible to prove existence and uniqueness when the friction coefficient is less than C varepsilon2 |log(h)|{-1}, where h and varepsilon denote the discretization and regularization parameters, respectively. This bound converging very slowly towards 0 when h decreases (in comparison with the already known results of the non-regularized case) suggests a minor dependence of the mesh size on the uniqueness conditions, at least for practical engineering computations. Then we study the solutions of a simple finite element example in the non-regularized case. It can be shown that one, multiple or an infinity of solutions may occur and that, for a given loading, the number of solutions may eventually decrease when the friction coefficient increases.

5

Variational Analysis of a Frictional Contact Problem for the Bingham Fluid

Awbi B., Selmani L., Sofonea M.

International Journal of Applied Mathematics and Computer Science

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1999

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Vol. 9, no 2

371-385

EN

We consider a mathematical model which describes the flow of a Bingham fluid with friction. We assume a stationary flow and we model the contact with damped response and a local version of Coulomb's law of friction.The problem leads to a quasi-variational inequality for the velocity field. We establish the existence of a weak solution and, under additional assumptions, its uniqueness. The proofs are based on a new result obtained in (Motreanu and Sofonea, 1999). We also establish the continuous dependence of the solution with respect to the contact conditions.