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 Contact
Index. 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 31
Côte 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 Contact
Index. 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 31
Côte titre :	MAM/0785