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A Viscoelastic Frictionless Contact Problem with Adhesion

100%
Touzaline A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2015
|
tom 63
|
nr 1
53-66
EN
We consider a mathematical model which describes the equilibrium between a viscoelastic body in frictionless contact with an obstacle. The contact is modelled with normal compliance, associated with Signorini's conditions and adhesion. The adhesion is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove the existence and uniqueness of the weak solution. The proof is based on arguments of evolution equations with multivalued maximal monotone operators, differential equations and the Banach fixed point theorem.
2
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A quasistatic contact problem with unilateral constraint and slip-dependent friction

100%
Touzaline A.
Applicationes Mathematicae
|
2015
|
tom 42
|
nr 2-3
167-182
EN
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.
3
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A study of a unilateral and adhesive contact problem with normal compliance

100%
Touzaline A.
Applicationes Mathematicae
|
2014
|
tom 41
|
nr 4
385-402
EN
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 formulation of the mechanical problem and prove an existence and uniqueness result in the case where the friction coefficient is small enough. The technique of proof is based on time-dependent variational inequalities, differential equations and the Banach fixed-point theorem. We also study a penalized and regularized problem which admits at least one solution and prove its convergence to the solution of the model when the penalization and regularization parameter tends to zero.
4
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Study of a contact problem with normal compliance and nonlocal friction

100%
Touzaline A.
Applicationes Mathematicae
|
2012
|
tom 39
|
nr 1
43-55
EN
We consider a static frictional contact between a nonlinear elastic body and a foundation. The contact is modelled by a normal compliance condition such that the penetration is restricted with unilateral constraint and associated to the nonlocal friction law. We derive a variational formulation and prove its unique weak solvability if the friction coefficient is sufficiently small. Moreover, we prove the continuous dependence of the solution on the contact conditions. Also we study the finite element approximation of the problem and obtain an error estimate.
5
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Frictionless contact problem with adhesion and finite penetration for elastic materials

100%
Touzaline A.
Annales Polonici Mathematici
|
2010
|
tom 98
|
nr 1
23-38
EN
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 which is modelled by a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We derive a variational formulation of the mechanical problem and we establish an existence and uniqueness result by using arguments of time-dependent variational inequalities, differential equations and the Banach fixed-point theorem. Moreover, using compactness properties we study a regularized problem which has a unique solution and we obtain the solution of the original model by passing to the limit as the regularization parameter converges to zero.
6
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Analysis of a contact adhesive problem with normal compliance and nonlocal friction

100%
Touzaline A.
Annales Polonici Mathematici
|
2012
|
tom 104
|
nr 2
175-188
EN
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 an existence and uniqueness result under a smallness assumption on the friction coefficient by using arguments of time-dependent variational inequalities, differential equations and the Banach fixed-point theorem.
7
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A quasistatic contact problem with adhesion and friction for viscoelastic materials

100%
Touzaline A.
Applicationes Mathematicae
|
2010
|
tom 37
|
nr 1
39-52
EN
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 formulation of the mechanical problem and prove the existence and uniqueness of a weak solution if the friction coefficient is sufficiently small. The proof is based on time-dependent variational inequalities, differential equations and the Banach fixed point theorem.
8
Content available remote

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

100%
Touzaline A.
Applicationes Mathematicae
|
2009
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tom 36
|
nr 1
107-127
EN
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 small. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments, differential equations and the Banach fixed point theorem.
9
Content available remote

A unilateral contact problem with slip-dependent friction

100%
Touzaline A.
Applicationes Mathematicae
|
2016
|
tom 43
|
nr 1
105-116
EN
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 of an iterative method to the finite element problem.
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