Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion

Chau, Oanh; Fernández, José R.; Shillor, Meir; Sofonea, Mircea

doi:10.1016/s0377-0427(03)00547-8

Cited by 66 publications

(62 citation statements)

References 10 publications

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“…Moreover, [4,5], we introduce a surface state variable β, the bonding field, which is a measure of the fractional intensity of adhesion between the surface and the foundation. This variable is restricted to values 0 ≤ β ≤ 1; when β = 0 all the bonds are severed and there are no active bonds; when β = 1 all the bonds are active; when 0 < β < 1 it measures the fraction of active bonds, and partial adhesion takes place.…”

Section: The Model and Its Variational Formulationmentioning

confidence: 99%

“…Analysis of models for adhesive contact can be found in [4,5,6,14,16] and recently in the monographs [16,17]. The novelty in all the above papers is the introduction of a surface internal variable, the bonding field, denoted in this paper by β, it describes the pointwise fractional density of active bonds on the contact surface, and is sometimes referred to as the intensity of adhesion.…”

Section: Introductionmentioning

confidence: 99%

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A bilateral contact problem with adhesion and damage between two viscoelastic bodies

Derbazi¹,

Boukrioua²,

Dalah³

et al. 2016

J. Nonlinear Sci. Appl.

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This paper deals with the study of a mathematical model which describes the bilateral, frictionless adhesive contact between two viscoelastic bodies with damage. The adhesion of the contact surfaces is considered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness result of the solution. The proofs are based on time-dependent variational equalities, a classical existence and uniqueness result on parabolic equations, differential equations, and fixed-point arguments.

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Section: The Model and Its Variational Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A bilateral contact problem with adhesion and damage between two viscoelastic bodies

Derbazi¹,

Boukrioua²,

Dalah³

et al. 2016

J. Nonlinear Sci. Appl.

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show abstract

“…We use it in H ad , since usually when the glue is stretched beyond the limit L it does not contribute more to the bond strength. An example of such a function, used in [8], is…”

Section: Problem Statementmentioning

confidence: 99%

Variational Analysis and the Convergence of the Finite Element Approximation of an Electro-Elastic Contact Problem with Adhesion

Drabla

Zellagui

2011

Arab J Sci Eng

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A model for the adhesive, quasi-static and frictionless contact between an electro-elastic body and a rigid foundation is studied in this paper. The contact is modelled with Signorini's conditions with adhesion. We provide variational formulation for the problem and prove the existence of a unique weak solution to the model. The proofs are based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point. Then, a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. Error estimates are derived on the approximative solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions.

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“…Basic modeling can be found in [10][11][12]. Analysis of models for adhesive contact can be found in [7,8] and in the monographs [24,27]. An application of the theory of adhesive contact in the medical field of prosthetic limbs was considered in [22,23]; there, the importance of the bonding between the bone-implant and the tissue was outlined, since debonding may lead to decrease in the persons ability to use the artificial limb or joint.…”

Section: Introductionmentioning

confidence: 99%

A Quasistatic Electro-Viscoelastic Contact Problem with Adhesion

Chougui

Drabla

2015

Bull. Malays. Math. Sci. Soc.

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The aim of this paper is to study the process of contact with adhesion between a piezoelectric body and an obstacle, the so-called foundation. The material's behavior is assumed to be electro-viscoelastic; the process is quasistatic, the contact is modeled by the Signorini condition. The adhesion process is modeled by a bonding field on the contact surface. We derive a variational formulation for the problem and then we prove the existence of a unique weak solution to the model. The proof is based on a general result on evolution equations with maximal monotone operators and fixed-point arguments.

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Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion

Cited by 66 publications

References 10 publications

A bilateral contact problem with adhesion and damage between two viscoelastic bodies

A bilateral contact problem with adhesion and damage between two viscoelastic bodies

Variational Analysis and the Convergence of the Finite Element Approximation of an Electro-Elastic Contact Problem with Adhesion

A Quasistatic Electro-Viscoelastic Contact Problem with Adhesion

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