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Probabilistic prediction of the quality factor of micro-resonator using a stochastic thermo-mechanical multi-scale approach
Wu, Ling; Lucas, Vincent; Golinval, Jean-Claude et al.
201615th edition of the European Mechanics of Materials Conference (EMMC15)
 

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Keywords :
Stochastic; multi-scale; polycrystalline; LIMARC
Abstract :
[en] As the size of the device is only one or two orders of magnitude higher than the size of the grains, the structural properties, such as the thermo-elastic quality factor (Q), of micro-electro-mechanical systems (MEMS) made of poly-crystalline materials exhibit a scatter, due to the existing randomness in the grain size, grain orientation, surface roughness... In order to predict the probabilistic behavior of micro-resonators, the authors extend herein a previously developed stochastic 3-scale approach [1] to the case of thermoelastic damping [2]. In this method, stochastic volume elements (SVEs) [3] are defined by considering random grain orientations in a tessellation. For each SVE realization, the mesoscopic apparent elasticity tensor, thermal conductivity tensor, and thermal dilatation tensor can be obtained using thermo-mechanical computational homogenization theory [4]. The extracted mesoscopic apparent properties tensors can then be used to define a spatially correlated meso-scale random field, which is in turn used as input for stochastic finite element simulations. As a result, the probabilistic distribution of the quality factor of micro-resonator can be extracted by considering Monte-Carlo simulations of coarse-meshed micro-resonators, accounting implicitly for the random micro-structure of the poly-silicon material. [1] V. Lucas, J.-C. Golinval, S. Paquay, V.-D. Nguyen, L. Noels, L. Wu, A stochastic computational multiscale approach; Application to MEMS resonators. Computer Methods in Applied Mechanics and Engineering, 294, 141-167, 2015. [2] L. Wu, V. Lucas, V.-D. Nguyen, J.-C. Golinval, S. Paquay, L. Noels, A Stochastic Multiscale Approach for the Modeling of Thermoelastic Damping in Micro-Resonators. Submitted. [3] M. Ostoja-Starzewski, X.Wang, Stochastic finite elements as a bridge between random material microstructure and global response, Computer Methods in Applied Mechanics and Engineering, 168, 35--49, 1999. [4] I. Özdemir, W. A. M. Brekelmans, M. G. D. Geers, Computational homogenization for heat conduction in heterogeneous solids, International Journal for Numerical Methods in Engineering 73, 185-204, 2008.
Disciplines :
Mechanical engineering
Materials science & engineering
Author, co-author :
Wu, Ling ;  Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Lucas, Vincent ;  Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Golinval, Jean-Claude  ;  Université de Liège > Département d'aérospatiale et mécanique > LTAS - Vibrations et identification des structures
Paquay, Stéphane;  Open Engineering SA
Noels, Ludovic  ;  Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Language :
English
Title :
Probabilistic prediction of the quality factor of micro-resonator using a stochastic thermo-mechanical multi-scale approach
Publication date :
07 September 2016
Event name :
15th edition of the European Mechanics of Materials Conference (EMMC15)
Event organizer :
European Mechanics Society (Euromech)
Event place :
Brussels, Belgium
Event date :
7-9th September 2016
Audience :
International
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
Available on ORBi :
since 12 October 2016

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