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Modélisation multi-échelles de structures hétérogènes aux comportements anélastiques non-linéaires

Abstract : In design of civil and mechanical engineering structures it is very important to be able to adequately predict their failure mechanisms. However, materials used are often strongly heterogeneous, like for instance the concrete or metalic composites, and are consequently difficult to model when submitted to extreme loading. In this work we propose a new multi scale strategy adapted for this kind of problems. According to the approach we couple a finite element method (FEM) model at the structural scale (micro) with a very fine model at the scale of the microstructure (micro), also based on the FEM. It allows us to model the micro scale much more accurately than what is possible with phenomenological approaches or analytical homogenisation methods. Since in general the major incovenience of such an approach is a very high computational cost, we consider three aspects which enable its application to realistic situations. First of all, the variational formulation allows for using the fine model only in parts of the structure, where the scales are really strongly coupled, whereas we use a homogenised model elsewhere. In addition, we adapt the FEM on the micro scale by employing the so called structured approach, with which we can significanlty reduce the number of degrees of freedom by retaining the came accuracy. The third aspect concerns the implementation of the method in a finite element code, adapted for parallel machines, with which we could run analyses of a size comparable to realistic situations. Finally, we show in which way this approach can bc used for inclusion shape optimisation of a composite material.
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https://tel.archives-ouvertes.fr/tel-00133643
Contributor : Ens Cachan Bibliothèque <>
Submitted on : Tuesday, February 27, 2007 - 11:20:00 AM
Last modification on : Monday, February 15, 2021 - 10:49:47 AM
Long-term archiving on: : Saturday, May 14, 2011 - 2:35:14 AM

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  • HAL Id : tel-00133643, version 1

Citation

Damijan Markovic. Modélisation multi-échelles de structures hétérogènes aux comportements anélastiques non-linéaires. Matériaux. École normale supérieure de Cachan - ENS Cachan, 2004. Français. ⟨tel-00133643⟩

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