Abstract :
[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].
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[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.