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Développements de la méthode des éléments finis avec des points d'intégration Lagrangiens : applications à la géomécanique

Abstract : Many numerical models in geophysics, civil engineering and mechanical engineering need to take into account large deformation on materials with behaviour ranked from viscous to elastic, with or without granular or layered microstructure, passing by two phase materials. A new numerical method named finite element method with Lagrangian interpolation points (FEMLIP) has been developped to answer this problem. This method is based on an Eulerian finite element mesh with Lagrangian particles carrying material properties and time variables. Thus, large deformation limits have been abolished and history variables can be carried through the mesh. The implicit desciption of material interfaces gives the possibility to model fluid-solid interactions by assigning contrasted rheological properties to particles in space. This work has shown that constrains on particle number and on particle numerical weights are required to get accurate results on benchmarks. Because of large transformations incrementally treated, this method implies a particular attention while developping and implementing new constitutive laws. During this work, the Cosserat theory, viscoelasticity, non linear models and anisotropy, eventually coupled with the Cosserat theory, have been implemented to answer specific models of geophysics and material working processes. The FEMLIP has shown its capacity to model material flows in large deformation and a great potential for further applications.
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Contributor : Frédéric Dufour <>
Submitted on : Friday, October 24, 2008 - 2:31:15 PM
Last modification on : Thursday, November 19, 2020 - 3:54:37 PM
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  • HAL Id : tel-00334013, version 1

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CNRS | 3S-R | UGA

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Frédéric Dufour. Développements de la méthode des éléments finis avec des points d'intégration Lagrangiens : applications à la géomécanique. Matériaux. Ecole Centrale de Nantes (ECN); Université de Nantes, 2002. Français. ⟨tel-00334013⟩

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