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Contribution à la modélisation de phénomènes de frontière libre en mécanique des films minces

Abstract : This work is devoted to the mathematical analysis, the modelling and the numerical analysis of interfaces problems in thin films mechanics. Liquid-gas interfaces problems such as cavitation appear in most of lubricated devices and the modelling of such phenomena is highly discussed in tribology. Variational inequalities have been widely used (it is still the case) but the non-conservative properties of this model have led to the introduction of an heuristic model based on an elliptic-hyperbolic system (the so-called Elrod-Adams model). However, this modelling also contains some open questions as one focuses on realistic regimes. Among theses difficulties:
1/ the possibility to use this model when the surfaces are rough. From a mathematical point of view, this deals with the homogenization study of a pressure-saturation problem,
2/ the elastic deformation of the solid surfaces due to high peaks of the hydrodynamic pressure. For this, the introduction of modified coefficients is widely used in elastohydrodynamic lubrication (E.H.L.): indeed, a nonlocal integral term (Hertz-type deformation) is considered. Cavitation is still taken into account in the hydrodynamic part and, consequently, on the whole coupling.
3/ the possibility to justify the modelling from a rigorous bifluid description of the flow and get a way to compute friction coefficients in the thin film flow.

We focus on these aspects which allow to conclude on the well-posedness of the cavitation modelling.
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Contributor : Sébastien Martin <>
Submitted on : Tuesday, January 3, 2006 - 10:25:10 AM
Last modification on : Wednesday, July 8, 2020 - 12:43:14 PM
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  • HAL Id : tel-00011279, version 1


Sébastien Martin. Contribution à la modélisation de phénomènes de frontière libre en mécanique des films minces. Mathématiques [math]. INSA de Lyon, 2005. Français. ⟨tel-00011279⟩



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