Bilateral Contact Problem With Friction and Wear for an Electro Elastic-Viscoplastic Materials With Damage

Djabi, Abdelmoumene; Merouani, Abdelbaki

doi:10.11650/tjm.19.2015.5453

Cited by 4 publications

(5 citation statements)

References 11 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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“…To illustrate the procedure of deformation of an elastic-viscoplastic body with wear when it contacts with a rigid body foundation, been touched on many quasi-static elastic-viscoplastic frictional Contact problems involving wear have been introduced and investigated under various conditions. For further details, we direct the reader to [5,6] and the cited references therein.…”

Section: Introductionmentioning

confidence: 99%

A quasistatic elastic-viscoplastic contact problem with wear and frictionless

Hamidat,

Adel Aissaoui

2023

Malaya J. Mat.

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We consider here a frictionless contact problem for elastic-viscoplastic materials, in a quasi-static process. The contact with a rigid base is modeled without friction with condition of wear and damage. The damage the elastic deformations of the material is modeled by an internal variable of the body called the damage field. The problem formula is given as a system that includes a variational equation with respect to the displacement field, and a variational inequality of the parabolic type with respect to the damage field. We prove a weak solution existence and uniqueness theorem relating to the problem. The techniques employed are based on the theory of monotonic operators, followed by fixed point arguments.

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“…Different models have been developed to describe the interaction between the thermal and mechanical field see [3,11]. A thermo elastic-viscoplastic body is considered in [6,11].…”

Section: Introductionmentioning

confidence: 99%

A dynamic Tresca's frictional contact problem with damage for thermo elastic-viscoplastic bodies

Boukaroura

Djabi

2019

Stud. Univ. Babes-Bolyai Math.

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We consider a dynamic contact problem between an elastic-viscoplastic body and a rigid obstacle. The contact is frictional and bilateral, the friction is modeled with Tresca's law with heat exchange. We employ the elastic-viscoplastic with damage constitutive law for the material. The evolution of the damage is described by an inclusion of parabolic type. We establish a variational formulation for the model and we prove the existence of a unique weak solution to the problem. The proof is based on a classical existence and uniqueness result on parabolic inéqualities, differentiel equations and fixed point argument.

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Bilateral Contact Problem With Friction and Wear for an Electro Elastic-Viscoplastic Materials With Damage

Cited by 4 publications

References 11 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

A quasistatic elastic-viscoplastic contact problem with wear and frictionless

A dynamic Tresca's frictional contact problem with damage for thermo elastic-viscoplastic bodies

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