Variational analysis of an electro viscoelastic contact problem with friction

Lerguet, Z.; Zellagui, Ziloukha; Benseridi, Hamid; Drabla, Salah

doi:10.1016/j.jaubas.2012.10.001

Cited by 10 publications

(6 citation statements)

References 6 publications

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“…Duvaut and Lions were the first to work on the mathematical theory of contact mechanics; They introduced variational formulations of contact problems and provided existence and uniqueness results. Subsequently, several new works have focused on the resolution of these variational problems such as the work of Refs [1][2][3][4][5][6]. However, mathematical theory of contact problems is a very broad field of study where many issues remain to be investigated.…”

Section: Introductionmentioning

confidence: 99%

“…Recent researches use coupled laws of behavior between mechanical and electric effects or between mechanical and thermal effects. For the case of coupled laws of behavior between mechanical and electric effects, numerous papers use different electro-mechanical conditions such as [2,5,7,8]. For the case of coupled laws of behavior between mechanical and thermal effects, we can found several models in Refs [4,6,7,[9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…Recent modeling, analysis and numerical simulations of electro-mechanical, thermomechanical and thermo-electro-mechanical contact problems with friction can be found in Refs [2,4,5,7,10,11,14]. General models of energy can be found in Refs [1].…”

Section: Introductionmentioning

confidence: 99%

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A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material

Djabi

2023

AJMS

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PurposeThe paper presents a mathematical problem involving quasistatic contact between a thermo-electro-viscoelastic body and a lubricated foundation, where the contact is described using a version of Coulomb’s law of friction that includes normal damped response conditions and heat exchange with a conductive foundation. The constitutive law for the material is thermo-electro-viscoelastic. The problem is formulated as a system that includes a parabolic equation of the first kind for the temperature, an evolutionary elliptic quasivariational inequality for the displacement and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments.Design/methodology/approachThe author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.FindingsThe author proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.Originality/valueThe author studies a mathematical problem between a thermo-electro-viscoelastic body and a lubricated foundation using a version of Coulomb’s law of friction including the normal damped response conditions and the heat exchange with a conductive foundation, which is original and requires a good understanding of modeling and mathematical tools.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material

Djabi

2023

AJMS

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“…General models for elastic materials with piezoelectric effects can be found in [5,14]. Dynamic contact problems are the topic of numerous papers, e.g.…”

Section: Introductionmentioning

confidence: 99%

Variational Analysis of an Electro-Elasto-Viscoplastic Contact Problem With Friction and Wear

Rimi

Ammar

2021

Comm. Math. Appl.

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We consider a dynamic contact problem with wear between two elastic-viscoplastic piezoelectric bodies. The contact is frictional and bilateral which results in the wear of contacting surface. The evolution of the wear function is described with Archard's law. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed point arguments.

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“…For a more in-depth exploration of this subject, we recommend consulting the findings presented in the research work [5,13,23,30]. The motivation behind this work lies in addressing the dynamic bi-frictional contact challenges encountered by thermo-electro-viscoelastic materials.…”

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confidence: 99%

On the problem of dynamic bi-frictional contact of thermo-electro-viscoelastic materials

Meziane,

Boulaaras,

Hadj-ammar

et al. 2024

DCDS-S

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In this work, we will investigate a contact problem that arises in the interaction of two thermo-electro-viscoelastic bodies with adhesion and damage. The bilateral contact is modeled through Tresca's friction law, and the materials undergo damage as a result of elastic deformations. The existence and uniqueness of the weak solution is obtained through the derivation of a variational formulation. The proof mainly relies on the results of variable evolutionary inequalities, ordinary differential equations and fixed-point theory.

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Variational analysis of an electro viscoelastic contact problem with friction

Cited by 10 publications

References 6 publications

A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material

A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material

Variational Analysis of an Electro-Elasto-Viscoplastic Contact Problem With Friction and Wear

On the problem of dynamic bi-frictional contact of thermo-electro-viscoelastic materials

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