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Stochastic multiscale method applied to thermo-elasticity of polycrystalline micro-structures
Wu, Ling; Lucas, Vincent; Golinval, Jean-Claude et al.
20172017 Engineering Mechanics Institute Conference (EMI 2017)
 

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Keywords :
Multi-scale; Stochastic; Polycrystalline Materials; Thermoelasticity; Quality Factor
Abstract :
[en] A stochastic 3-scale approach is developed in order to predict the probabilistic behavior of micro-resonators made of polycrystalline materials. In this method, stochastic volume elements (SVEs) [1] are defined from Voronoï tessellations using experimental measurements of the grain size, orientation, and surface roughness [2]. For each SVE realization, the mesoscopic apparent thermo-elastic properties such as elasticity tensor, thermal conductivity tensor, and thermal dilatation tensor are extracted using a coupled homogenization theory [3, 4]. A stochastic model is then built from the homogenized properties extracted from Voronoï tessellations using a moving window technique in order to generate spatially correlated meso-scale random fields. These random fields are then used as input for stochastic finite element simulations. As a result, the probabilistic distribution of micro-resonator properties can be extracted. The applications are two-fold: either a stochastic thermo-elastic homogenization is coupled to thermo-elastic 3D models of the micro-resonator in order to extract the probabilistic distribution of the Quality factor of the micro-resonators [5], or a stochastic second-order mechanical homogenization is coupled to a plate model of the micro-resonator in order to extract the effect of the uncertainties related to the surface roughness of the polycrystalline structures [1]. References [1] Lucas, V., Golinval, J.-C., Voicu, R., Danila, M., Gravila, R., Muller, R., Dinescu, A., Noels, L., & Wu, L. (in press). Propagation of material and surface profile uncertainties on MEMS micro-resonators using a stochastic second-order computational multi-scale approach. International Journal for Numerical Methods in Engineering. [2] Ostoja-Starzewski, M., Wang, X. (1999) Stochastic finite elements as a bridge between random material microstructure and global response, Computer Methods in Applied Mechanics and Engineering, 168, 35-49, 1999 [3] Temizer, I., Wriggers, P. (2011) Homogenization in finite thermoelasticity, Journal of the Mechanics and Physics of Solids 59 (2), 344-372 [4] Nguyen, V. D., Wu, L., Noels, L. (in press). Unified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method. Computational Mechanics. [5] Wu, L., Lucas, V., Nguyen, V. D., Golinval, J.-C., Paquay, S., & Noels, L. (2016) A Stochastic Multi-Scale Approach for the Modeling of Thermo-Elastic Damping in Micro-Resonators. Computer Methods in Applied Mechanics & Engineering, 310, 802-839.
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 - ULiège > 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 :
Stochastic multiscale method applied to thermo-elasticity of polycrystalline micro-structures
Publication date :
05 June 2017
Event name :
2017 Engineering Mechanics Institute Conference (EMI 2017)
Event organizer :
Engineering Mechanics Institute
Event place :
San Diego, United States
Event date :
4-7 June 2017
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
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
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