1. A class of dynamic contact problems with Coulomb friction in viscoelasticity
- Author
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Marius Cocou, Matériaux et Structures (M&S), Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Européen Associé CNRS Franco-Roumain de Mathématiques et Modélisation LEA Math-Mode, and Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)
- Subjects
Surface (mathematics) ,Work (thermodynamics) ,set-valued mapping ,Fixed-point theorem ,Unilateral contact ,MSC(2010): 35Q74, 49J40, 74A55, 74D05, 74H20 ,[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph] ,Type (model theory) ,01 natural sciences ,Viscoelasticity ,Dynamic problem ,pointwise conditions ,0101 mathematics ,viscoelasticity ,Mathematics ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,General Engineering ,General Medicine ,010101 applied mathematics ,Computational Mathematics ,Coulomb friction ,Classical mechanics ,Compact space ,Dynamic problems ,General Economics, Econometrics and Finance ,Analysis - Abstract
International audience; The aim of this work is to study a class of nonsmooth dynamic contact problem which model several surface interactions, including relaxed unilateral contact conditions, adhesion and Coulomb friction laws, between two viscoelastic bodies of Kelvin-Voigt type. An abstract formulation which generalizes these problems is considered and the existence of a solution is proved by using Ky Fan's fixed point theorem, suitable approximation properties, several estimates and compactness arguments.
- Published
- 2015
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