scholarly journals Existence and uniqueness for a quasistatic frictional bilateral contact problem in thermoviscoelasticity

2000 ◽  
Vol 58 (3) ◽  
pp. 543-560 ◽  
Author(s):  
M. Rochdi ◽  
M. Shillor
Keyword(s):  
Contact Problem ◽  
Existence And Uniqueness ◽  
Bilateral Contact

Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Othmane Baiz ◽  
Hicham Benaissa ◽  
Zakaria Faiz ◽  
Driss El Moutawakil
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Contact Problem ◽  
Existence And Uniqueness ◽  
Frictional Contact ◽  
Hemivariational Inequalities ◽  
Frictional Contact Problem ◽  
Uniqueness Of A Solution

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.

A piezoelectric contact problem with slip dependent friction and damage

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abderrezak Kasri
Keyword(s):  
Weak Solution ◽  
Contact Problem ◽  
Dry Friction ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Normal Compliance ◽  
Electrically Conductive ◽  
Coulomb’S Law ◽  
Electrical Condition ◽  
Coulomb's Law

Abstract 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.

scholarly journals An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

2013 ◽  
Vol 23 (2) ◽  
pp. 263-276 ◽  
Author(s):  
Mikaël Barboteu ◽  
Krzysztof Bartosz ◽  
Piotr Kalita
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Numerical Approach ◽  
Bundle Method ◽  
Nonconvex Problem ◽  
Proximal Bundle Method ◽  
Loss Of Contact ◽  
The Galerkin Method ◽  
Bilateral Contact ◽  
Numerical Approaches

We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.

scholarly journals Existence and uniqueness of the weak solution for a contact problem

2016 ◽  
Vol 09 (01) ◽  
pp. 186-199
Author(s):  
Amar Megrous ◽  
Ammar Derbazi ◽  
Mohamed Dalah
Keyword(s):  
Weak Solution ◽  
Contact Problem ◽  
Existence And Uniqueness

A traction contact problem governed by hemivariational inequalities for a mixed formulation of Stokes equation

2016 ◽  
Vol 22 (3) ◽  
pp. 420-433 ◽  
Author(s):  
T Sluzalec
Keyword(s):  
Weak Solution ◽  
Velocity Field ◽  
Contact Problem ◽  
Stokes Equation ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Contact Problems ◽  
Mixed Formulation ◽  
Hemivariational Inequalities ◽  
The Stokes Equation

In this paper the traction contact problems for Stokes equation are discussed and the Stokes equation is considered in a mixed formulation. We prove the existence and uniqueness of the weak solution for a mixed formulation of Stokes equation with traction contact. The traction contact is described by subdifferential boundary conditions. For this problem we present a variational formulation in a form of a hemivariational inequality for the velocity field.

scholarly journals Analysis of a frictionless contact problem for elastic-viscoplastic materials

2012 ◽  
Vol 17 (1) ◽  
pp. 99-117
Author(s):  
Mohamed Selmani ◽  
Lynda Selmani
Keyword(s):  
Contact Problem ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Order Differential Equation ◽  
Nonlinear Evolution ◽  
Monotone Operators ◽  
Uniqueness Result ◽  
Nonlinear Evolution Equations ◽  
Frictionless Contact ◽  
First Order

We consider a dynamic frictionless contact problem for elastic-viscoplastic materials with damage. The contact is modelled with normal compliance condition. The adhesion of the contact surfaces is considered and is modelled with a surface variable, the bonding field whose evolution is described by a first order differential equation. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed-point arguments.

The Boundary-Contact Problem of Elasticity for Homogeneous Anisotropic Media with a Contact on Some Part of the Boundaries

1995 ◽  
Vol 2 (2) ◽  
pp. 111-123
Author(s):  
O. Chkadua
Keyword(s):  
Contact Problem ◽  
Potential Theory ◽  
Existence And Uniqueness ◽  
Anisotropic Media ◽  
Bessel Potential ◽  
Manifolds With Boundary ◽  
Uniqueness Of Solutions ◽  
Pseudodifferential Equations ◽  
Boundary Contact

Abstract The existence and uniqueness of solutions of the boundary-contact problem of elasticity for homogeneous anisotropic media with a contact on some part of their boundaries are investigated in the Besov and Bessel potential classes using the methods of the potential theory and the theory of pseudodifferential equations on manifolds with boundary. The smoothness of the solutions obtained is studied.

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