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.

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.

A QUASISTATIC UNILATERAL CONTACT PROBLEM WITH FRICTION FOR NONLINEAR ELASTIC MATERIALS

2007 ◽  
Vol 12 (4) ◽  
pp. 497-514 ◽  
Author(s):  
Arezki Touzaline ◽  
Djamel Eddine Teniou
Keyword(s):  
Friction Coefficient ◽  
Contact Problem ◽  
Dry Friction ◽  
Unilateral Contact ◽  
Elastic Materials ◽  
Existence Of A Solution ◽  
Coulomb’S Law ◽  
Nonlinear Elastic ◽  
Coulomb's Law

The aim of this paper is to prove the existence of a solution to the quasistatic unilateral contact problem with a modified version of Coulomb's law of dry friction for nonlinear elastic materials. We derive a variational incremental problem which admits a solution if the friction coefficient is sufficiently small and then by passing to the limit with respect to time we obtain the existence of a solution.

A PIEZOELECTRIC CONTACT PROBLEM WITH SLIP DEPENDENT COEFFICIENT OF FRICTION

2004 ◽  
Vol 9 (3) ◽  
pp. 229-242 ◽  
Author(s):  
M. Sofonea
Keyword(s):  
Mathematical Model ◽  
Weak Solution ◽  
Contact Problem ◽  
Coefficient Of Friction ◽  
Dry Friction ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Coupled System ◽  
Piezoelectric Body ◽  
The Coefficient Of Friction

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an obstacle. The constitutive relation of the material is assumed to be electroelastic and involves a nonlinear elasticity operator. The contact is modelled with a version of Coulomb's law of dry friction in which the coefficient of friction depends on the slip. We derive a variational formulation for the model which is in form of a coupled system involving as unknowns the displacement field and the electric potential. Then we provide the existence of a weak solution to the model and, under a smallness assumption, we provide its uniqueness. The proof is based on a result obtained in [14] in the study of elliptic quasi‐variational inequalities.

The Motion of a Rolling Polygon

2003 ◽  
Vol 70 (2) ◽  
pp. 275-280 ◽  
Author(s):  
E. M. Beunder ◽  
P. C. Rem
Keyword(s):  
Angular Velocity ◽  
Dry Friction ◽  
Coulomb’S Law ◽  
Inclined Surface ◽  
Coulomb's Law

Galileo was the first to analyze the motion of spheres rolling down an inclined surface. Since then, Coulomb’s law of dry friction has covered the case of sliding particles. However, a particle that is not round can still roll, although in a way that is essentially different from the motion studied by Galileo. Instead of keeping contact with the surface, such particles will start bouncing after reaching a certain angular velocity. This motion is a combination of flying and colliding. It is shown that the acceleration of a bouncing particle is always bounded by the accelerations for perfect rolling and sliding. In order to describe the motion of a not perfectly round particle, the polygon is used as a model. The aim of the model is to predict the trajectories of particles that cannot be covered by the models for perfect rolling and sliding.

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

scholarly journals VARIATIONAL ANALYSIS OF A FRICTIONAL CONTACT PROBLEM WITH WEAR AND DAMAGE

2021 ◽  
Vol 26 (2) ◽  
pp. 170-187
Author(s):  
Mohammed Salah Mesai Aoun ◽  
Mohamed Selmani ◽  
Abdelaziz Azeb Ahmed
Keyword(s):  
Long Memory ◽  
Dry Friction ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Variational Analysis ◽  
Friction And Wear ◽  
Frictional Contact ◽  
Constitutive Law ◽  
Quasistatic Problem ◽  
Elliptic Variational Inequalities

We study a quasistatic problem describing the contact with friction and wear between a piezoelectric body and a moving foundation. The material is modeled by an electro-viscoelastic constitutive law with long memory and damage. The wear of the contact surface due to friction is taken into account and is described by the differential Archard condition. The contact is modeled with the normal compliance condition and the associated law of dry friction. We present a variational formulation of the problem and establish, under a smallness assumption on the data, the existence and uniqueness of the weak solution. The proof is based on arguments of parabolic evolutionary inequations, elliptic variational inequalities and Banach fixed point.

scholarly journals Variational and Numerical Analysis for Frictional Contact Problem with Normal Compliance in Thermo-Electro-Viscoelasticity

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Mustapha Bouallala ◽  
El Hassan Essoufi ◽  
Mohamed Alaoui
Keyword(s):  
Contact Problem ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Approximate Solutions ◽  
Numerical Approach ◽  
Normal Compliance ◽  
Fully Discrete ◽  
Tresca’S Friction ◽  
Discrete Finite Element ◽  
Finite Element Schemes

In this paper, we consider a mathematical model of a contact problem in thermo-electro-viscoelasticity with the normal compliance conditions and Tresca’s friction law. We present a variational formulation of the problem, and we prove the existence and uniqueness of the weak solution. We also study the numerical approach using spatially semidiscrete and fully discrete finite element schemes with Euler’s backward scheme. Finally, we derive error estimates on the approximate solutions.

scholarly journals A dynamic electroviscoelastic problem with thermal effects

2021 ◽  
Vol 66 (4) ◽  
pp. 769-781
Author(s):  
Sihem Smata ◽  
◽  
Nemira Lebri ◽  
Keyword(s):  
Thermal Effects ◽  
Dry Friction ◽  
Variational Formulation ◽  
Classical Result ◽  
Monotone Operators ◽  
Constitutive Law ◽  
Unique Weak Solution ◽  
Electrically Conductive ◽  
Piezoelectric Body ◽  
Signorini Condition

We consider a mathematical model which describes the dynamic pro- cess of contact between a piezoelectric body and an electrically conductive foun- dation. We model the material's behavior with a nonlinear electro-viscoelastic constitutive law with thermal e ects. Contact is described with the Signorini condition, a version of Coulomb's law of dry friction. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear rst order evolution inequali- ties, the equations with monotone operators, and the xed point arguments.

Analysis of a sliding frictional contact problem with unilateral constraint

2016 ◽  
Vol 22 (3) ◽  
pp. 324-342 ◽  
Author(s):  
Mircea Sofonea ◽  
Yahyeh Souleiman
Keyword(s):  
Contact Problem ◽  
Dry Friction ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Convergence Result ◽  
Uniqueness Result ◽  
Unilateral Constraint ◽  
Penalization Method ◽  
Result Theorem ◽  
Equivalence Result

We consider a mathematical model that describes the equilibrium of an elastic body in frictional contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with unilateral constraint, associated with a sliding version of Coulomb’s law of dry friction. We present a description of the model, list the assumptions on the data and derive its primal variational formulation, in terms of displacement. Then we prove an existence and uniqueness result, Theorem 3.1. We proceed with a penalization method in the study of the contact problem for which we present a convergence result, Theorem 4.1. Finally, under additional hypotheses, we consider a variational formulation of the problem in terms of the stress, the so-called dual variational formulation, and prove an equivalence result, Theorem 5.3. The proofs of the theorems are based on arguments of monotonicity, compactness, convexity and lower semicontinuity.

Sign in / Sign up

Export Citation Format

Share Document