Doctoral thesis (Dissertations and theses)
Stochastic multi-scale modelling of MEMS
Lucas, Vincent
2016
 

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Keywords :
Stochastic; Multi-scale; MEMS
Abstract :
[en] When studying Micro-Electro-Mechanical Systems (or MEMS) made of poly-crystalline materials, as the size of the device is only one or two orders of magnitude higher than the size of the grains, the structural properties exhibit a scatter at the macro-scale due to the existing randomness in the grain size, grain orientation, surface roughness... In order to predict the probabilistic behaviour at the structural scale, we investigated the recourse to a stochastic 3-scale approach in this thesis dissertation. Estimating the scatter in the response of the structure is studied at macro-scale based on stochastic finite elements along with Monte-Carlo simulations. To produce accurate results, the mesh size of the finite element approach should be small enough so that the heterogeneities can be captured. This can lead to overwhelming computation if the microstructure is directly considered, thus justifying the recourse to stochastic homogenisation to define a meso-scale random field. Based on a stochastic model of this random field, the variability of the response of the structure can be computed. In this work, the micro-scale uncertainties are modelled based on measurements provided by the IMT-Bucharest institute. These uncertainties are then propagated towards the macro-scale for 3 different problems. The first one serves the purpose of verification. The variability of the resonance frequency of a micro-beam is computed and compared to a reference numerical solution. The second problem extends the 3-scale approach to the thermo-elastic case. Thus the uncertainties of the quality factor of 3D beams are studied with a modelling of the anchor. Finally, the third problem aims at propagating surface roughness uncertainties on the resonance frequency of thin plates.
Research center :
Computational & Multiscale Mechanics of Materials
Disciplines :
Mechanical engineering
Author, co-author :
Lucas, Vincent ;  Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Language :
English
Title :
Stochastic multi-scale modelling of MEMS
Defense date :
29 August 2016
Institution :
ULiège - Université de Liège
Degree :
Docteur en sciences de l'ingénieur
Promotor :
Noels, Ludovic  ;  Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)
President :
Golinval, Jean-Claude  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique
Jury member :
Yvonnet, Julien
Vandepitte, Dirk
Arnst, Maarten ;  Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)
Wu, Ling ;  Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
Name of the research project :
3SMVIB: The research has been funded by the Walloon Region under the agreement no 1117477 (CT-INT 2011-11-14) in the context of the ERA-NET MNT framework.
Funders :
Service public de Wallonie : Direction générale opérationnelle de l'économie, de l'emploi et de la recherche - DG06 ; CECI
Available on ORBi :
since 18 September 2016

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