Displaying similar documents to “Study of a contact problem with normal compliance and nonlocal friction”

A unilateral contact problem with slip-dependent friction

Arezki Touzaline (2016)

Applicationes Mathematicae

Similarity:

We consider a mathematical model which describes a static contact between a nonlinear elastic body and an obstacle. The contact is modelled with Signorini's conditions, associated with a slip-dependent version of Coulomb's nonlocal friction law. We derive a variational formulation and prove its unique weak solvability. We also study the finite element approximation of the problem and obtain an optimal error estimate under extra regularity for the solution. Finally, we establish the convergence...

Analysis and Numerical Approximation of an Electro-elastic Frictional Contact Problem

El. Essoufi, El. Benkhira, R. Fakhar (2010)

Mathematical Modelling of Natural Phenomena

Similarity:

We consider the problem of frictional contact between an piezoelectric body and a conductive foundation. The electro-elastic constitutive law is assumed to be nonlinear and the contact is modelled with the Signorini condition, nonlocal Coulomb friction law and a regularized electrical conductivity condition. The existence of a unique weak solution of the model is established. The finite elements approximation for the problem is presented, ...

Analysis of a contact adhesive problem with normal compliance and nonlocal friction

Arezki Touzaline (2012)

Annales Polonici Mathematici

Similarity:

The paper deals with the problem of a quasistatic frictional contact between a nonlinear elastic body and a deformable foundation. The contact is modelled by a normal compliance condition in such a way that the penetration is restricted with a unilateral constraint and associated to the nonlocal friction law with adhesion. The evolution of the bonding field is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove...

A quasistatic contact problem with unilateral constraint and slip-dependent friction

Arezki Touzaline (2015)

Applicationes Mathematicae

Similarity:

We consider a mathematical model of a quasistatic contact between an elastic body and an obstacle. The contact is modelled with unilateral constraint and normal compliance, associated to a version of Coulomb's law of dry friction where the coefficient of friction depends on the slip displacement. We present a weak formulation of the problem and establish an existence result. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments.

Analysis and numerical approximation of an elastic frictional contact problem with normal compliance

Weimin Han, Mircea Sofonea (1999)

Applicationes Mathematicae

Similarity:

We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show...

Analysis of a frictionless contact problem for elastic bodies

S. Drabla, M. Sofonea, B. Teniou (1998)

Annales Polonici Mathematici

Similarity:

This paper deals with a nonlinear problem modelling the contact between an elastic body and a rigid foundation. The elastic constitutive law is assumed to be nonlinear and the contact is modelled by the well-known Signorini conditions. Two weak formulations of the model are presented and existence and uniqueness results are established using classical arguments of elliptic variational inequalities. Some equivalence results are presented and a strong convergence result involving a penalized...

A quasistatic contact problem with adhesion and friction for viscoelastic materials

Arezki Touzaline (2010)

Applicationes Mathematicae

Similarity:

We consider a mathematical model which describes the contact between a deformable body and a foundation. The contact is frictional and is modelled by a version of normal compliance condition and the associated Coulomb's law of dry friction in which adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behaviour is modelled by a nonlinear viscoelastic constitutive law. We derive a variational...

A study of a unilateral and adhesive contact problem with normal compliance

Arezki Touzaline (2014)

Applicationes Mathematicae

Similarity:

The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational...

Quasistatic frictional problems for elastic and viscoelastic materials

Oanh Chau, Dumitru Motreanu, Mircea Sofonea (2002)

Applications of Mathematics

Similarity:

We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution...

A frictional contact problem with adhesion for viscoelastic materials with long memory

Abderrezak Kasri (2021)

Applications of Mathematics

Similarity:

We consider a quasistatic contact problem between a viscoelastic material with long-term memory and a foundation. The contact is modelled with a normal compliance condition, a version of Coulomb's law of dry friction and a bonding field which describes the adhesion effect. We derive a variational formulation of the mechanical problem and, under a smallness assumption, we establish an existence theorem of a weak solution including a regularity result. The proof is based on the time-discretization...

The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory

Ammar Derbazi, Mohamed Dalah, Amar Megrous (2016)

Applications of Mathematics

Similarity:

We study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, and the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field...