University Sétif 1 FERHAT ABBAS Faculty of Sciences
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Titre : An Analytical Study Of Quasistatic Frictionless Antiplane Problem With Adhesion Type de document : document électronique Auteurs : Amina Arab, Auteur ; Laldja Benziane, Directeur de thèse Editeur : Sétif:UFA1 Année de publication : 2025 Importance : 1 vol (31 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Antiplane Shear
Viscoelastic Material
Adhesion Contact
Frictionless ContactIndex. décimale : 510-Mathématique Résumé : Abstract
In this thesis, we consider a mathematical model describing the antiplane shear deformation of a cylinder in frictionless
contact with a rigid foundation. The adhesion between the contact surfaces, induced by a bonding agent, is explicitly
accounted for. The material is assumed to be viscoelastic with long-term memory and nonhomogeneous properties, and
the process is modeled as quasistatic. This work is devided into three chapters. First, we present preliminary results from
functional analysis and partial differential equations, which lay the mathematical foundation for the subsequent
analysis. Next, the second chapter focuses on the mathematical modeling of the antiplane shear deformation problem,
incorporating adhesion effects, viscoelasticity with long-term memory, and matterial nonhomogeneity under
quasistatic assumptions. Finally, the third chapter establishes a variational formulation of the coupled system, a
volterra-type variational equality for the displacement field and an evolution equation for the bonding field..Note de contenu : Contents
Abstract i
Acknowledgements ii
Introduction 1
1 MathematicalTools 3
1.1 FunctionSpaces . ...................................... 3
1.1.1 TheSpaces Cm(Ω) and Lp(Ω) . .......................... 3
1.1.2 TheSobolevSpaces . ............................... 6
1.1.3 Equivalentnormsonthespace H1(Ω) . ...................... 6
1.2 BilinearForminHilbertSpaces . ............................. 7
1.3 DiverseAdditions . ..................................... 8
1.4 Someinequalities . ..................................... 9
1.5 Volterra-typeVariationalEquality . ............................ 10
1.6 Convexfunctions-lowersemi-continuity . ........................ 11
2 MathematicalModelingofAntiplaneShearDeformation 12
2.1 MathematicalModel . ................................... 12
2.2 AFunctionSpaceforAntiplaneProblems . ........................ 17
3 AntiplaneProblemforViscoelasticwithLong-TermMemoryMaterial 20
3.1 MechanicalFormulationoftheProblemandHypotheses . ................ 20
3.1.1 MechanicalFormulation . ............................. 20
3.1.2 Hypotheses . .................................... 21
3.1.3 Variationalformulation . .............................. 23
3.1.4 ProofofTheorem 3.2 . ............................... 25
Conclusion 31Côte titre : MAM/0785 An Analytical Study Of Quasistatic Frictionless Antiplane Problem With Adhesion [document électronique] / Amina Arab, Auteur ; Laldja Benziane, Directeur de thèse . - [S.l.] : Sétif:UFA1, 2025 . - 1 vol (31 f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Antiplane Shear
Viscoelastic Material
Adhesion Contact
Frictionless ContactIndex. décimale : 510-Mathématique Résumé : Abstract
In this thesis, we consider a mathematical model describing the antiplane shear deformation of a cylinder in frictionless
contact with a rigid foundation. The adhesion between the contact surfaces, induced by a bonding agent, is explicitly
accounted for. The material is assumed to be viscoelastic with long-term memory and nonhomogeneous properties, and
the process is modeled as quasistatic. This work is devided into three chapters. First, we present preliminary results from
functional analysis and partial differential equations, which lay the mathematical foundation for the subsequent
analysis. Next, the second chapter focuses on the mathematical modeling of the antiplane shear deformation problem,
incorporating adhesion effects, viscoelasticity with long-term memory, and matterial nonhomogeneity under
quasistatic assumptions. Finally, the third chapter establishes a variational formulation of the coupled system, a
volterra-type variational equality for the displacement field and an evolution equation for the bonding field..Note de contenu : Contents
Abstract i
Acknowledgements ii
Introduction 1
1 MathematicalTools 3
1.1 FunctionSpaces . ...................................... 3
1.1.1 TheSpaces Cm(Ω) and Lp(Ω) . .......................... 3
1.1.2 TheSobolevSpaces . ............................... 6
1.1.3 Equivalentnormsonthespace H1(Ω) . ...................... 6
1.2 BilinearForminHilbertSpaces . ............................. 7
1.3 DiverseAdditions . ..................................... 8
1.4 Someinequalities . ..................................... 9
1.5 Volterra-typeVariationalEquality . ............................ 10
1.6 Convexfunctions-lowersemi-continuity . ........................ 11
2 MathematicalModelingofAntiplaneShearDeformation 12
2.1 MathematicalModel . ................................... 12
2.2 AFunctionSpaceforAntiplaneProblems . ........................ 17
3 AntiplaneProblemforViscoelasticwithLong-TermMemoryMaterial 20
3.1 MechanicalFormulationoftheProblemandHypotheses . ................ 20
3.1.1 MechanicalFormulation . ............................. 20
3.1.2 Hypotheses . .................................... 21
3.1.3 Variationalformulation . .............................. 23
3.1.4 ProofofTheorem 3.2 . ............................... 25
Conclusion 31Côte titre : MAM/0785 Exemplaires (1)
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