Displaying similar documents to “A study of a unilateral and adhesive contact problem with normal compliance”

Frictionless contact problem with adhesion and finite penetration for elastic materials

Arezki Touzaline (2010)

Annales Polonici Mathematici

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The paper deals with the problem of quasistatic frictionless contact between an elastic body and a foundation. The elasticity operator is assumed to vanish for zero strain, to be Lipschitz continuous and strictly monotone with respect to the strain as well as Lebesgue measurable on the domain occupied by the body. The contact is modelled by normal compliance in such a way that the penetration is limited and restricted to unilateral contraints. In this problem we take into account adhesion...

A quasistatic contact problem with adhesion and friction for viscoelastic materials

Arezki Touzaline (2010)

Applicationes Mathematicae

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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...

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

Arezki Touzaline (2012)

Annales Polonici Mathematici

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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...

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

Weimin Han, Mircea Sofonea (1999)

Applicationes Mathematicae

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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...

Quasistatic frictional problems for elastic and viscoelastic materials

Oanh Chau, Dumitru Motreanu, Mircea Sofonea (2002)

Applications of Mathematics

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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 quasistatic contact problem with unilateral constraint and slip-dependent friction

Arezki Touzaline (2015)

Applicationes Mathematicae

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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.

A viscoelastic contact problem with normal damped response and friction

B. Awbi, El H. Essoufi, M. Sofonea (2000)

Annales Polonici Mathematici

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We study an evolution problem which describes the quasistatic contact of a viscoelastic body with a foundation. We model the contact with normal damped response and a local friction law. We derive a variational formulation of the model and we establish the existence of a unique weak solution to the problem. The proof is based on monotone operators and fixed point arguments. We also establish the continuous dependence of the solution on the contact boundary conditions.

Analysis of a frictionless contact problem for elastic bodies

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

Annales Polonici Mathematici

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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...

Analysis of a viscoelastic antiplane contact problem with slip-dependent friction

Thierry-Vincent Hoarau-Mantel, Andaluzia Matei (2002)

International Journal of Applied Mathematics and Computer Science

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We study a mathematical problem modelling the antiplane shear deformation of a viscoelastic body in frictional contact with a rigid foundation. The contact is bilateral and is modelled with a slip-dependent friction law. We present the classical formulation for the antiplane problem and write the corresponding variational formulation. Then we establish the existence of a unique weak solution to the model, by using the Banach fixed-point theorem and classical results for elliptic variational...

A quasistatic bilateral contact problem with adhesion and friction for viscoelastic materials

Arezki Touzaline (2010)

Commentationes Mathematicae Universitatis Carolinae

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We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca's friction law in which adhesion is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behavior is modelled with a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness...

Study of a viscoelastic frictional contact problem with adhesion

Arezki Touzaline (2011)

Commentationes Mathematicae Universitatis Carolinae

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We consider a quasistatic frictional contact problem between a viscoelastic body with long memory and a deformable foundation. The contact is modelled with normal compliance in such a way that the penetration is limited and restricted to unilateral constraint. The adhesion between contact surfaces is taken into account and the evolution of the bonding field is described by a first order differential equation. We derive a variational formulation and prove the existence and uniqueness...

Quasistatic problems in contact mechanics

Meir Shillor (2001)

International Journal of Applied Mathematics and Computer Science

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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...