Propagation of uncertainties in the modelling of MEMS resonators (using a 3-scale probabilistic approach)

In order to ensure the accuracy of MEMS vibrometers, the first resonance frequency should be predicted at the design phase. However, this prediction is subjected to randomness: there is a scatter in the reached value resulting from the uncertainties involved in the manufacturing process. The purpose of this work is to take into account these uncertainties of the microstructure. The objective is a non-deterministic model that can be used since the design stage. The material is the source of uncertainties: the beam resonator is made of a polycrystalline material in which each grain has a random orientation. Solving the problem with a full direct numerical simulation combined to a Monte-Carlo method allows the probability density function of the resonance frequency to be computed. However this methodology is computationally expensive due to the number of degrees of freedom required to study one sample, motivating the development of a computationally efficient method. Towards this end a 3-scales stochastic model for predicting the resonance frequency of a micro-beam made of a polycrystalline linear anisotropic material is described. At the lower scale, we model the micro-structure with micro-volume elements. Due to the small-scale involved, the representativity of these micro-volume elements is not achieved and thus Statistical Volume Elements (SVE) are considered. These SVEs are generated under the form of a Voronoï tessellation, each grain being assigned a random orientation. Computational homogenization is applied over the SVEs, along with a Monte-Carlo procedure, to obtain a stochastic characterization of the elasticity tensor at the second scale of interest, the meso-scale. The spatial correlation between SVEs is also estimated. A generator based on spectral methods is implemented. Afterwards, using a stochastic finite element method, these meso-scale uncertainties are propagated by taking account of the spatial correlation up to the higher scale to predict the probabilistic behavior of the MEMS resonator.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

A stochastic 3-scale method to predict the thermo-elastic behaviors of polycrystalline structures

The purpose of this work is to upscale material uncertainties in the context of thermo-elastic response of polycrystalline structures. The probabilistic behavior of micro-resonators made of polycrystalline materials is evaluated using a stochastic multi-scale approach defined using the following methodology. 1. Stochastic volume elements (SVEs) [1] are defined from Voronoi tessellations using experimental measurements of the grain size, orientation, and surface roughness [2]; 2. 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] applied on the SVE realizations; 3. A stochastic model of the homogenized properties extracted from Voronoi tessellations using a moving window technique is then constructed in order to be able to generate spatially correlated meso-scale random fields; 4. These meso-scale 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: 1. A stochastic thermo-elastic homogenization, see Fig. 1(a), 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, see Fig. 1(b), 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 [2]. References [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, 802-839.3SMVIB: 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. Experimental measurements provided by IMT Bucharest (Voicu Rodica, Baracu Angela, Muller Raluca

A stochastic computational multiscale approach; Application to MEMS resonators

peer reviewedThe 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.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

Probabilistic prediction of the quality factor of micro-resonator using a stochastic thermo-mechanical multi-scale approach

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, 2008.3SMVIB: 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

Experimental validation of opto-thermo-elastic modeling in OOFELIE Multiphysics

The objective of this work is to demonstrate the correlation between a simple laboratory test bench case and the predictions of the Oofelie MultiPhysics software in order to deduce modelling guidelines and improvements. For that purpose two optical systems have been analysed. The first one is a spherical lens fixed in an aluminium barrel, which is the simplest structure found in an optomechanical system. In this study, material characteristics are assumed to be well known: BK7 and aluminium have been retained. Temperature variations between 0 and +60°C from ambient have been applied to the samples. The second system is a YAG laser bar heated by means of a dedicated oven. For the two test benches thermo-elastic distortions have been measured using a Fizeau interferometer. This sensor measures wavefront error in the range of 20 nm to 1 μm without physical contact with the optomechanical system. For the YAG bar birefringence and polarization measurements have also been performed using a polarimetric bench. The tests results have been compared to the predictions obtained by Oofelie MultiPhysics which is a multiphysics toolkit treating coupled problems of optics, mechanics, thermal physics, electricity, electromagnetism, acoustics and hydrodynamics. From this comparison modelling guidelines have been issued with the aim of improving the accuracy of computed thermo-elastic distortions and their impact on the optical performances

Probabilistic prediction of the quality factor of micro-resonator using a stochastic thermo-mechanical multi-scale approach

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 to the case of thermoelastic damping. In this method, stochastic volume elements (SVEs) 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. The extracted mesoscopic apparent properties tensors can then be used to define a spatially correlated mesoscale 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 microstructure of the poly-silicon material.3SMVIB: The research has been funded by the Walloon Region under the agreement no 1117477 (CT-INT 2011-11-14) and by Romanian UEFISCDI Agency contract ERA-NET MNT no 7-063/2012 (20122015) in the context of the ERA-NET MNT framewor

Specific Oncogenic Activity of the Src-Family Tyrosine Kinase c-Yes in Colon Carcinoma Cells

c-Yes, a member of the Src tyrosine kinase family, is found highly activated in colon carcinoma but its importance relative to c-Src has remained unclear. Here we show that, in HT29 colon carcinoma cells, silencing of c-Yes, but not of c-Src, selectively leads to an increase of cell clustering associated with a localisation of β-catenin at cell membranes and a reduction of expression of β-catenin target genes. c-Yes silencing induced an increase in apoptosis, inhibition of growth in soft-agar and in mouse xenografts, inhibition of cell migration and loss of the capacity to generate liver metastases in mice. Re-introduction of c-Yes, but not c -Src, restores transforming properties of c-Yes depleted cells. Moreover, we found that c-Yes kinase activity is required for its role in β-catenin localisation and growth in soft agar, whereas kinase activity is dispensable for its role in cell migration. We conclude that c-Yes regulates specific oncogenic signalling pathways important for colon cancer progression that is not shared with c-Src

Développement d'une méthodologie de simulation numérique pour les problèmes vibro-acoustiques couplés intérieurs/extérieurs de grande taille

D'une manière générale, nous pouvons dire que l'objectif principal de la thèse réside dans la conception d'une méthodologie de résolution efficace de systèmes vibro-acoustiques intérieurs et extérieurs en couplage fort. La modélisation de systèmes vibro-acoustiques réels nécessite beaucoup de ressources informatiques tant au niveau du calcul qu'au niveau de l'espace mémoire. Avec la montée en puissance des ordinateurs, bon nombre d'applications industrielles peuvent enfin être simulées. Des techniques de modélisation avancées comme la méthode p [17] appliquée aux cavités acoustiques sont très efficaces et permettent aussi une augmentation du degré de raffinement d'un problème vibro-acoustique, à puissance machine équivalente, bien entendu. Au niveau des techniques de résolution, les choses peuvent probablement encore évoluer. Actuellement, la résolution directe du problème aux valeurs propres des systèmes structure-cavité se fait généralement par la formulation mixte en potentiel des déplacements/pression selon l'argument que seuls les algorithmes symétriques de résolution sont efficaces. Toutefois, bon nombre d'algorithmes non-symétriques jouissant de très bonnes performances ont été développés aux cours des dernières années (bi-itération, Lanczos nonsymétrique,...). Ainsi, nous avons développé un algorithme de recherche de solutions propres adapté à la formulation non-symétrique et comparé ses performances à celui de la formulation mixte symétrique. Dans le cadre des méthodes modales, les bases découplées sont largement utilisées industriellement pour la résolution des systèmes structure-cavité en excitation forcée. Cependant, la précision dépend fortement du nombre de modes découplés pris en compte quand le couplage est fort. L'utilisation de la base couplée semble dès lors plus judicieuse. Des méthodologies de projection dans la base couplée doivent donc être implémentées. Pour le rayonnement acoustique externe, la méthode variationnelle des éléments de frontière reste la plus utilisée. Toutefois, le caractère plein du système matriciel résultant pose de réelles difficultés pour la résolution de systèmes de grande taille. Cette limitation pourra être levée par l'utilisation d'un algorithme itératif [2] en lieu et place de la méthode de résolution directe. Par ailleurs, la méthode variationnelle reste très lente si le maillage présente peu de régularité".--Résumé abrégé par UMI

Développement d'une méthodologie de simulation numérique pour les problèmes vibro-acoustiques couplés intérieurs/extérieurs de grande taille

D'une manière générale, nous pouvons dire que l'objectif principal de la thèse réside dans la conception d'une méthodologie de résolution efficace de systèmes vibro-acoustiques intérieurs et extérieurs en couplage fort. La modélisation de systèmes vibro-acoustiques réels nécessite beaucoup de ressources informatiques tant au niveau du calcul qu'au niveau de l'espace mémoire. Avec la montée en puissance des ordinateurs, bon nombre d'applications industrielles peuvent enfin être simulées. Des techniques de modélisation avancées comme la méthode p [17] appliquée aux cavités acoustiques sont très efficaces et permettent aussi une augmentation du degré de raffinement d'un problème vibro-acoustique, à puissance machine équivalente, bien entendu. Au niveau des techniques de résolution, les choses peuvent probablement encore évoluer. Actuellement, la résolution directe du problème aux valeurs propres des systèmes structure-cavité se fait généralement par la formulation mixte en potentiel des déplacements/pression selon l'argument que seuls les algorithmes symétriques de résolution sont efficaces. Toutefois, bon nombre d'algorithmes non-symétriques jouissant de très bonnes performances ont été développés aux cours des dernières années (bi-itération, Lanczos nonsymétrique,...). Ainsi, nous avons développé un algorithme de recherche de solutions propres adapté à la formulation non-symétrique et comparé ses performances à celui de la formulation mixte symétrique. Dans le cadre des méthodes modales, les bases découplées sont largement utilisées industriellement pour la résolution des systèmes structure-cavité en excitation forcée. Cependant, la précision dépend fortement du nombre de modes découplés pris en compte quand le couplage est fort. L'utilisation de la base couplée semble dès lors plus judicieuse. Des méthodologies de projection dans la base couplée doivent donc être implémentées. Pour le rayonnement acoustique externe, la méthode variationnelle des éléments de frontière reste la plus utilisée. Toutefois, le caractère plein du système matriciel résultant pose de réelles difficultés pour la résolution de systèmes de grande taille. Cette limitation pourra être levée par l'utilisation d'un algorithme itératif [2] en lieu et place de la méthode de résolution directe. Par ailleurs, la méthode variationnelle reste très lente si le maillage présente peu de régularité".--Résumé abrégé par UMI