Displaying similar documents to “A Viscoelastic Frictionless Contact Problem with Adhesion”

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 frictionless contact problem for elastic-viscoplastic materials with internal state variable

Lynda Selmani (2013)

Applicationes Mathematicae

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We study a mathematical model for frictionless contact between an elastic-viscoplastic body and a foundation. We model the material with a general elastic-viscoplastic constitutive law with internal state variable and the contact with a normal compliance condition. We derive a variational formulation of the model. We establish existence and uniqueness of a weak solution, using general results on first order nonlinear evolution equations with monotone operators and fixed point arguments....

A quasistatic unilateral and frictional contact problem with adhesion for elastic materials

Arezki Touzaline (2009)

Applicationes Mathematicae

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We consider a quasistatic contact problem between a linear elastic body and a foundation. The contact is modelled with the Signorini condition and the associated non-local Coulomb friction law in which the adhesion of the contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation of the mechanical problem and prove existence of a weak solution if the friction coefficient is sufficiently...

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...

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.

A frictional contact problem with wear and damage for electro-viscoelastic materials

Mohamed Selmani, Lynda Selmani (2010)

Applications of Mathematics

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We consider a quasistatic contact problem for an electro-viscoelastic body. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. The damage of the material caused by elastic deformation is taken into account, its evolution is described by an inclusion of parabolic type. We present a weak formulation for the model and establish existence and uniqueness results. The proofs are based on classical results for elliptic...

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

Abderrezak Kasri (2021)

Applications of Mathematics

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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...

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

Arezki Touzaline (2014)

Applicationes Mathematicae

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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...

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...

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.