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Etude théorique et numérique de la propagation d'ondes en présence de contact unilatéral dans un milieu fissuré

Abstract : The diffraction of elastic waves by a crack is a serious issue in nondestructive testing. A realistic model consists in taking into account unilateral contact conditions on the crack. In this thesis, we focus on dynamic unilateral contact problems for cracked bodies. We first consider a cracked viscoelastic body with Kelvin-Voigt model, for which we have unilateral contact boundary conditions with nonlocal friction. We derive an existence result by using a penalty method and compactness results. Numerical results deal with the elastodynamic problem with unilateral contact condition without friction. To solve it, we use the fictitious domain method where the unknowns are stresses, displacements and Lagrange multipliers. A specific finite element is used for space discretization which allows to obtain a time explicit scheme by mass lumping. Several time discretization schemes are described: an off-centered implicit scheme is proved to be stable and a centered implicit scheme appears to be stable through the numerical results. Results of validation and results dealing with more realistic applications are given.
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https://tel.archives-ouvertes.fr/tel-00006272
Contributor : Gilles Scarella <>
Submitted on : Tuesday, June 15, 2004 - 3:24:58 PM
Last modification on : Thursday, February 11, 2021 - 2:50:06 PM
Long-term archiving on: : Friday, April 2, 2010 - 8:54:31 PM

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Gilles Scarella. Etude théorique et numérique de la propagation d'ondes en présence de contact unilatéral dans un milieu fissuré. Mathématiques [math]. Université Paris Dauphine - Paris IX, 2004. Français. ⟨tel-00006272⟩

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