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

Drabla, Salah; Zellagui, Ziloukha

doi:10.1007/s13369-011-0131-z

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…Note that we need to impose assumption (2.12) for physical reasons. Indeed, this condition models the case when the obstacle is a perfect insulator and was used in [3,9]. Condition (2.7) represents the bilateral contact, where u ν represents the normal displacement.…”

Section: The Modelmentioning

confidence: 99%

Analysis of quasistatic viscoelastic viscoplastic piezoelectric contact problem with friction and adhesion

Chougui¹

2022

Stud. Univ. Babes-Bolyai Math.

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"In this paper we study the process of bilateral contact with adhesion and friction between a piezoelectric body and an insulator obstacle, the socalled foundation. The material's behavior is assumed to be electro-viscoelastic- viscoplastic; the process is quasistatic, the contact is modeled by a general non-local friction law with adhesion. The adhesion process is modeled by a bonding field on the contact surface. We derive a variational formulation for the problem and then, under a smallness assumption on the coe cient of friction, we prove the existence of a unique weak solution to the model. The proofs are based on a general results on elliptic variational inequalities and fixed point arguments."

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Section: The Modelmentioning

confidence: 99%

Analysis of quasistatic viscoelastic viscoplastic piezoelectric contact problem with friction and adhesion

Chougui¹

2022

Stud. Univ. Babes-Bolyai Math.

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“…Note that we need to impose assumption (2.12) for physical reasons. Indeed, this condition models the case when the obstacle is a perfect insulator and was used in [1,9,15,25,26]. The evolution of the bonding field is governed by the differential Eq.…”

Section: Problem 1 (P) Find a Displacement Field Umentioning

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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“…Some general models for electro-elastic materials can be found in [3,4]. A static frictional contact problem for electro-elastic materials was considered in [5,6].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Frictionless Electro Viscoelastic Contact Problem with Signorini Conditions

Boulaouad

Ourahmoun

Serrar

2022

Eng. Technol. Appl. Sci. Res.

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This study considered a mathematical model to describe the process of a quasi-static contact between a piezoelectric body and an electrically conductive foundation. The behavior of the material was modeled with a nonlinear electro-viscoelastic constitutive law, the contact was frictionless, and the result was described with the Signorini condition. A variational formulation was derived for the problem, proving the existence and uniqueness of a weak solution of the model. The proof was based on arguments for nonlinear equations with maximal monotone operators.

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

Cited by 5 publications

References 14 publications

Analysis of quasistatic viscoelastic viscoplastic piezoelectric contact problem with friction and adhesion

Analysis of quasistatic viscoelastic viscoplastic piezoelectric contact problem with friction and adhesion

A Quasistatic Electro-Viscoelastic Contact Problem with Adhesion

Analysis of a Frictionless Electro Viscoelastic Contact Problem with Signorini Conditions

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