# Modélisation et méthodes de décomposition de domaines pour des problèmes de contact

Abstract : This PhD thesis treats the mathematical modelization of thin layers and the domain decomposition methods in contact mechanics.\\
The first part is dedicated to a quasistatic contact problem with non local Coulomb friction law between an elastic body and a thin layer. After establishing an existence theorem, we define a critical ratio between the geometrical and the elastic parameters. For this ratio, we establish rigorously a limit contact law by making the layer thickness tends to zero.\\
The second part is devoted to some natural'' domain decomposition methods in contact problems. This method consists of retaining the natural interface between two bodies as a numerical interface for the domain decomposition. Firstly, we study a contact problem without friction between two elastic bodies (Signorini problem) for which we propose and prove the convergence of a Neumann-Dirichlet algorithm. This result is then generalized to a contact problem with Coulomb friction. At last, we propose and prove the convergence of a Neumann-Neumann'' decomposition algorithm for a Signorini problem.
Some numerical results give confidence to the validity of the theoretical results.
Keywords :
Document type :
Theses
Mathématiques [math]. INSA de Lyon, 2004. Français
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Cited literature [20 references]

https://tel.archives-ouvertes.fr/tel-00011970
Contributor : Jalila Sabil <>
Submitted on : Friday, March 17, 2006 - 12:32:31 PM
Last modification on : Tuesday, June 12, 2018 - 10:33:36 AM
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• HAL Id : tel-00011970, version 1

### Citation

Jalila Sabil. Modélisation et méthodes de décomposition de domaines pour des problèmes de contact. Mathématiques [math]. INSA de Lyon, 2004. Français. 〈tel-00011970〉

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