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1

A piezoelectric contact problem with slip dependent friction and damage

Kasri Abderrezak

Journal of Applied Analysis

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2021

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Vol. 27, nr 1

73--86

EN

The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.

2

Modeling and Numerical Simulation of a Unilateral Contact Problem with Slip-dependent Friction

Barboteu M., Danan D., Sofonea M.

Machine Dynamics Research

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2013

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Vol. 37, No. 1

15-28

EN

We construct a mathematical model which describes the contact between an elastic body and an obstacle, the so-called foundation. The contact is frictional and is modelled with normal compliance and unilateral constraint, associated to a slip- dependent version of Coulomb’s law of dry friction. We present a detailed description Of the model, then we provide numerical simulations in the study of a two-dimensional Example. Our aim is to underline the influence of the parameters involved in the boundary conditions, which could give rise to different status of the material points c>n the contact surface.

3

An Elastic Contact Problem with Normal Compliance and Memory Term

Barboteu M., Ramadan A., Sofonea M. T., Patrulescu F.

Machine Dynamics Research

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2012

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Vol. 36, No. 1

24-34

EN

We consider a history-dependent problem which describes the contact between an elastic body and an obstacle, the so-called foundation. The contact is frictionless and is modeled with a version of the normal compliance condition in which the memory effects are taken into account. The mathematical analysis of the problem, including existence, uniqueness and convergence results, was provided in (Barboteu et al., in preparation). Here we present the analytic expression of the solution and numerical simulations, in the study of one and two-dimensional examples, respectively.

4

A Contact Problem with Normal Compliance, Finite Penetration and Unilateral Constraint

Barboteu M., Sofonea M.

Machine Dynamics Research

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2011

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Vol. 35, No. 1

60-69

EN

We consider a quasistatic problem which describes the contact between a viscoplastic body and an obstacle, the so-called foundation. The contact is frictionless and is modelled with a version of the normal compliance condition in which the penetration is restricted with unilateral constraint. The mathematical analysis of the problem, including, existence, uniqueness and convergence results, was provided by Barboteu et al. (2011). Here we present numerical simulations in the study of an academic two-dimensional contact example.

5

An elastic contact problem with adhesion and normal compliance

Sofonea M., Matei A.

Journal of Applied Analysis

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2006

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Vol. 12, nr 1

19-36

EN

We study a mathematical problem describing the friction- less adhesive contact between an elastic body and a foundation. The adhesion process is modelled by a surface variable, the bonding field, and the contact is modelled with a normal compliance condition; the tangential shear due to the bonding field is included; the elastic consti- tutive law is assumed to be nonlinear and the process is quasistatic. The problem is formulated as a nonlinear system in which the unknowns are the displacement, the stress and the bonding field. The existence of a unique weak solution for the problem is established by using arguments for differential equations followed by the construction of an appropriate contraction mapping.

6

Dynamic Contact Problems With Slip-Dependent Friction in Viscoelasticity

Ionescu I. R., Nguyen Q. L.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 1

71-80

EN

The dynamic evolution with frictional contact of a viscoelastic body is considered. The assumptions on the functions used in modelling the contact are broad enough to include both the normal compliance and the Tresca models. The friction law uses a friction coefficient which is a non-monotone function of the slip. The existence and uniqueness of the solution are proved in the general three-dimensional case.

7

Quasistatic Problems in Contact Mechanics

Shillor M.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 1

189-204

EN

We describe some of our recent results concerning the modeling and analysis of quasistatic contact problems between a deformable body and a foundation. We concentrate mainly on frictional contact, and in some of the problems thermal effects and the wear of the contacting surfaces are also taken into account. We describe the physical processes involved, the mathematical models, their variational formulation and then present statements of our results. We conclude with a description of some unresolved problems.

8

Numerical Analysis and Simulations of Quasistatic Frictionless Contact Problems

Fernandez Garcia J. R., Han W., Shillor M., Sofonea M.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 1

205-222

EN

A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.