A stochastic computational multiscale approach; Application to MEMS resonators

NOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering 294 (2015) 141–167, DOI: 10.1016/j.cma.2015.05.019

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Keywords :

Multi-scale; Stochastic; Finite-Elements; Polycrystalline; Resonance frequency; MEMS; LIMARC

Abstract :

[en] The aim of this work is to develop a stochastic multiscale model for polycrystalline materials, which accounts for the uncertainties in the micro-structure. At the finest scale, we model the micro-structure using a random Voronoi tessellation, each grain being assigned a random orientation. Then, we apply a computational homogenization procedure on statistical volume elements to obtain a stochastic characterization of the elasticity tensor at the meso-scale. A random field of the meso-scale elasticity tensor can then be generated based on the information obtained from the SVE simulations. Finally, using a stochastic finite element method, these meso-scale uncertainties are propagated to the coarser scale. As an illustration we study the resonance frequencies of MEMS micro-beams made of poly-silicon materials, and we show that the stochastic multiscale approach predicts results in agreement with a Monte Carlo analysis applied directly on the fine finite-element model, i.e. with an explicit discretization of the grains.

Research Center/Unit :

Computational & Multiscale Mechanics of Materials

Disciplines :

Materials science & engineering
Mechanical engineering

Author, co-author :

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 S.A.

Nguyen, Van Dung ; Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)

Noels, Ludovic ; Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)

Wu, Ling ; Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)

Language :

English

Title :

A stochastic computational multiscale approach; Application to MEMS resonators

Publication date :

01 September 2015

Journal title :

Computer Methods in Applied Mechanics and Engineering

ISSN :

0045-7825

eISSN :

1879-2138

Publisher :

Elsevier Science, Lausanne, Switzerland

Volume :

294

Pages :

141–167

Peer reviewed :

Peer Reviewed verified by ORBi

Tags :

CÉCI : Consortium des Équipements de Calcul Intensif

Additional URL :

http://dx.doi.org/10.1016/j.cma.2015.05.019

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 01 June 2015

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