Reference : A stochastic 3-scale method for polycrystalline materials
Scientific conferences in universities or research centers : Scientific conference in universities or research centers
Engineering, computing & technology : Materials science & engineering
http://hdl.handle.net/2268/221862
A stochastic 3-scale method for polycrystalline materials
English
Noels, Ludovic mailto [Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3) >]
3-Apr-2018
International
Mechanics and Design of Advanced Material and Structures Symposium
3-4 April 2018
Northwestern Polytechnical University
Xi'an
China
[en] Stochastic multiscale ; polycrystalline materials ; MEMS
[en] The purpose of this work is to upscale material uncertainties in the context of thermo-elastic response of polycrystalline structures using a stochastic multi-scale approach defined as follows
1. Stochastic volume elements (SVEs) [1] are built using Voronoi tessellations and experimental measurements of the grain size, orientation, and surface roughness [2];
2. Mesoscopic apparent thermo-elastic properties are extracted using a coupled homogenization theory [3, 4] applied on the generated SVEs;
3. A stochastic model of the homogenized properties extracted using a moving window technique is then constructed in order to generate spatially correlated meso-scale random fields;
4. The random fields are then used as input for stochastic finite elements.
As a result, the probabilistic distribution of micro-resonator properties is studied for two-fold applications:
1. A stochastic thermo-elastic homogenization is coupled to thermoelastic 3D models of the micro-resonator in order to extract the probabilistic distribution of the quality factor of micro-resonators [5];
2. A stochastic second-order mechanical homogenization is coupled to a plate model of the micro-resonator in order to extract the effect of the surface roughness of the polycrystalline structures [2].

[1] Ostoja-Starzewski, M., Wang, X. Stochastic finite elements as a bridge between random material microstructure and global response. Comput. Meth. in Appl. Mech. and
Eng. (1999) 168: 35-49.
[2] Lucas, V., Golinval, J.-C., Voicu, R., Danila, M., Gravila, R., Muller, R., Dinescu, A., Noels, L., Wu, L. Propagation of material and surface profile uncertainties on MEMS micro-resonators using a stochastic second-order computational multi-scale approach. Int. J. for Num. Meth. in Eng. (2017).
[3] Temizer, I., Wriggers, P. Homogenization in finite thermoelasticity. J. of the Mech. and Phys. of Sol. (2011) 59, 344{372.
[4] Nguyen, V. D., Wu, L., Noels, L. Unified treatment of boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method. Computat. Mech. (2017) 59, 483-505.
[5] Wu, L., Lucas, V., Nguyen, V. D., Golinval, J.-C., Paquay, S., Noels, L. A Stochastic Multi-Scale Approach for the Modeling of Thermo-Elastic Damping in Micro-Resonators. Comput. Meth. in Appl. Mech. and Eng. (2016) 310, 802-839.
Service public de Wallonie : Direction générale opérationnelle de l'économie, de l'emploi et de la recherche - DG06
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
Researchers
http://hdl.handle.net/2268/221862
FP7 ; 291826 - M-ERA.NET - From materials science and engineering to innovation for Europe.

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