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Modélisation, analyse et simulation de problèmes de contact en mécanique des solides et des fluides.

Abstract : The modelling of contact problems leads to significant difficulties either conceptual, mathematical or computational. Motivated by the prominent position held by contact phenomena, we are interested in the modelling, the analysis and the numerical experiments of contact problems in solid and fluid mechanics. In a first theoretical part, we study the asymptotic behavior of solutions of time-dependent variational problems arising in frictional contact mechanics. The second part is devoted to the control of computations quality in structural mechanics. In order to find a convenient formulation and to carry out a study of contact problems with the eXtended Finite Element Method (XFEM) we first obtain a residual a posteriori error estimator for the XFEM method in the linear case, another one for the unilateral contact problem with Coulomb friction approximated with a standard finite element method, and a third one for the latter problem approximated by a stabilized Lagrange multiplier method (i.e., which do not require any inf-sup condition). This part ends with a definition of unilateral contact with the XFEM followed by an a priori error analysis. The third part is concerned with numerical simulations in fluid mechanics, more precisely the contact treatment in the red blood cells dynamics in a twodimensional setting.
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https://tel.archives-ouvertes.fr/tel-00442074
Contributor : Vanessa Lleras <>
Submitted on : Friday, December 18, 2009 - 10:48:17 AM
Last modification on : Saturday, December 19, 2020 - 3:00:34 AM
Long-term archiving on: : Thursday, June 17, 2010 - 10:01:49 PM

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  • HAL Id : tel-00442074, version 1

Citation

Vanessa Lleras. Modélisation, analyse et simulation de problèmes de contact en mécanique des solides et des fluides.. Mathématiques [math]. Université de Franche-Comté, 2009. Français. ⟨tel-00442074⟩

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