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 A VISCOELASTIC CONTACT PROBLEM WITH ADHESION AND SURFACE MEMORY EFFECTS

2014 ◽  
Vol 19 (5) ◽  
pp. 607-626 ◽  
Author(s):  
Mircea Sofonea ◽  
Flavius Patrulescu
Keyword(s):  
Long Memory ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Viscoelastic Body ◽  
Uniqueness Result ◽  
Unilateral Constraint ◽  
Memory Effects ◽  
Constitutive Law ◽  
Classical Formulation ◽  
Viscoelastic Contact

We consider a mathematical model which describes the quasistatic contact between a viscoelastic body and an obstacle, the so-called foundation. The material's behavior is modelled with a constitutive law with long memory. The contact is with normal compliance, unilateral constraint, memory effects and adhesion. We present the classical formulation of the problem, then we derive its variational formulation and prove an existence and uniqueness result. The proof is based on arguments of variational inequalities and fixed point.

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.

Weak solvability of a piezoelectric contact problem

2009 ◽  
Vol 20 (2) ◽  
pp. 145-167 ◽  
Author(s):  
STANISŁAW MIGÓRSKI ◽  
ANNA OCHAL ◽  
MIRCEA SOFONEA
Keyword(s):  
Mathematical Model ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Constitutive Law ◽  
Potential Fields ◽  
Material Behaviour ◽  
Abstract Result ◽  
Electrically Conductive ◽  
Piezoelectric Body ◽  
Weak Solvability

We consider a mathematical model which describes the frictional contact between a piezoelectric body and a foundation. The material behaviour is modelled with a non-linear electro-elastic constitutive law, the contact is bilateral, the process is static and the foundation is assumed to be electrically conductive. Both the friction law and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is of the form of a system of two coupled hemi-variational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proof is based on an abstract result on operator inclusions in Banach spaces.

scholarly journals A CLASS OF QUASISTATIC CONTACT PROBLEMS FOR VISCOELASTIC MATERIALS WITH NONLOCAL COULOMB FRICTION AND TIME-DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 491-508 ◽  
Author(s):  
Si-sheng Yao ◽  
Nan-jing Huang
Keyword(s):  
Mathematical Model ◽  
Variational Inequality ◽  
Time Delay ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Contact Problems ◽  
Existence And Uniqueness Theorem ◽  
Differential Variational Inequality

In this paper, a mathematical model which describes the explicit time dependent quasistatic frictional contact problems is introduced and studied. The material behavior is described with a nonlinear viscoelastic constitutive law with time-delay and the frictional contact is modeled with nonlocal Coulomb boundary conditions. A variational formulation of the mathematical model is given, which is called a quasistatic integro-differential variational inequality. Using the Banach's fixed point theorem, an existence and uniqueness theorem of the solution for the quasistatic integro-differential variational inequality is proved under some suitable assumptions. As an application, an existence and uniqueness theorem of the solution for the dual variational formulation is also given.

scholarly journals Variational and Numerical Analysis of a Static Thermo-Electro-Elastic Problem with Friction

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Othman Baiz ◽  
Hicham Benaissa ◽  
Driss El Moutawakil ◽  
Rachid Fakhar
Keyword(s):  
Frictional Contact ◽  
A Priori ◽  
Finite Element Approximation ◽  
Elastic Problem ◽  
Constitutive Law ◽  
Element Approximation ◽  
Coulomb’S Friction ◽  
Elliptic Variational Inequalities ◽  
Thermally Conductive ◽  
Priori Error Estimates

We consider a mathematical model which describes a static frictional contact between a piezoelectric body and a thermally conductive obstacle. The constitutive law is supposed to be thermo-electro-elastic and the contact is modeled with normal compliance and a version of Coulomb’s friction law. We derive a variational formulation of the problem and we prove the existence and uniqueness of its solution. The proof is based on some results of elliptic variational inequalities and fixed point arguments. Furthermore, a finite element approximation and a priori error estimates are obtained.

A QUASISTATIC FRICTIONAL CONTACT PROBLEM WITH NORMAL DAMPED RESPONSE FOR THERMO-ELECTRO-ELASTIC-VISCOPLASTIC BODIES

2021 ◽  
Vol 10 (12) ◽  
pp. 3549-3568
Author(s):  
A. Hamidat ◽  
A. Aissaoui
Keyword(s):  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Contraction Mapping ◽  
Original Problem ◽  
Frictional Contact ◽  
Unique Fixed Point ◽  
Mathematical Problem ◽  
Response Condition ◽  
Electric Potential Field ◽  
Normal Damped Response

We consider a mathematical problem for quasistatic contact between a thermo-electro--elastic-viscoplastic body and an obstacle. The contact is modeled by a general normal damped response condition with friction law and heat exchange. We present a variational formulation of the problem and prove the existence and uniqueness of the weak solution. The proof is based on the formulation of four intermediate problems for the displacement field, the electric potential field and the temperature field, respectively. We prove the unique solvability of the intermediate problems, then we construct a contraction mapping whose unique fixed point is the solution of the original problem.

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.

scholarly journals Tribological Properties of Sapphire under Dry Friction against Chromium and Zirconium Ceramics

2022 ◽  
Author(s):  
V. Alisin
Keyword(s):  
Mechanical Properties ◽  
Modulus Of Elasticity ◽  
Dry Friction ◽  
Friction And Wear ◽  
Open Space ◽  
Frictional Contact ◽  
Friction Couple ◽  
Vickers Indent ◽  
Friction Units ◽  
Zirconium Ceramics

Abstract. The issues of sapphire friction and wear in contact with chrome steel and zirconium ceramics are discussed in this article. The kinetic microindentation method is used to study the mechanical properties of sapphire in frictional contact in modelling experiments on the indentation of a Vickers indent. Taking into account the anisotropy of the mechanical properties of sapphire, the influence of the load and orientation of the indent on the modulus of elasticity and hardness is analyzed. It has been established that, under dry friction conditions it is promising the use of zirconium ceramics in the supports of devices operating under conditions in which the use of lubricants is impossible. The possibility of using a friction couple of sapphire-zirconium ceramics in friction units operating in open space is noted.

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.

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