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A probabilistic model for predicting the uncertainties of the humid stiction phenomenon on hard materials Hoang Truong, Vinh ; Wu, Ling ; et al in Journal of Computational & Applied Mathematics (2015), 289 Stiction is a major failure in microelectromechanical system (MEMS) devices in which two contacting surfaces can remain stuck together because of the adhesive forces. Due to the difference between the ... [more ▼] Stiction is a major failure in microelectromechanical system (MEMS) devices in which two contacting surfaces can remain stuck together because of the adhesive forces. Due to the difference between the surfaces roughness and the adhesive force range, the real contact areas are usually smaller than the apparent one, resulting in a scatter in the adhesive forces. Consequently, the stiction is an uncertain phenomenon. In this work, we develop a probabilistic model to predict the uncertainties of stiction due to the capillary forces acting on stiff materials. This model contains two levels: at the deterministic level, the model can predict the pull-out adhesive contact forces for a given surface topology; at the probabilistic level, the model generates independent identically distributed surfaces on which the deterministic solution can be applied to evaluate the uncertainties related to the stiction phenomenon. [less ▲] Detailed reference viewed: 208 (84 ULg)A stochastic computational multiscale approach; Application to MEMS resonators Lucas, Vincent ; Golinval, Jean-Claude ; et al in Computer Methods in Applied Mechanics & Engineering (2015), 294 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 173 (113 ULg)A probabilistic multi-scale model for polycrystalline MEMS resonators Lucas, Vincent ; Wu, Ling ; et al Conference (2015, July 09) The size of micro-electro-mechanical systems (MEMS) is only one or two orders of magnitude higher than the size of their micro-structure, i.e. their grain size. As a result, the structural properties ... [more ▼] The size of micro-electro-mechanical systems (MEMS) is only one or two orders of magnitude higher than the size of their micro-structure, i.e. their grain size. As a result, the structural properties exhibit a scatter. As an example we study the beam resonator illustrated in Fig. 1(a), made of poly-silicon 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 to be computed as illustrated in Fig. 1(b). However this methodology is computationally expensive due to the number of degrees of freedom required to study one sample, motivating the development of a non-deterministic 3-scale approach [3]. In a multiscale approach, at each macro-point of the macro-structure, the resolution of a microscale boundary value problem relates the macro-stress tensor to the macro-strain tensor. At the micro-level, the macro-point is viewed as the center of a Representative Volume Element (RVE). The resolution of the micro-scale boundary problem can be performed using finite-element simulations, as in the computational homogenization framework, e.g. [2]. However, to be representative, the micro-volume-element should have a size much bigger than the microstructure size. In the context of the MEMS resonator, this representativity is lost and Statistical Volume Elements (SVE) are considered. These SVEs are generated under the form of a Voronoi tessellation with a random orientation for each silicon grain. Hence, a Monte-Carlo procedure combined with a homogenization technique allows a distribution of the material tensor at the meso-scale to be estimated. The correlation between the meso-scale material tensors of two SVEs separated by a given distance can also be evaluated. A generator at the meso-scale based on the spectral method [4] is implemented. The generator [3] accounts for a lower bound [1] of the meso-scale material tensor in order to ensure the existence of the second-order moment of the Frobenius norm of the generated material tensor inverse [5]. Using the random meso-scale field obtained with the meso-scale generator, which accounts for the spatial correlation, a Monte-Carlo method can be used at the macro-scale to predict the probabilistic behavior of the MEMS resonator. [less ▲] Detailed reference viewed: 41 (8 ULg)Propagation of uncertainties in the modelling of MEMS resonators (using a 3-scale probabilistic approach) Lucas, Vincent ; Wu, Ling ; Golinval, Jean-Claude et al Conference (2015, May 26) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 27 (6 ULg)A stochastic multiscale analysis for MEMS stiction failure Hoang Truong, Vinh ; Wu, Ling ; Golinval, Jean-Claude et al Conference (2015, May 26) Stiction is a major failure in microelectromechanical system (MEMS) devices in which two contacting surfaces can remain stuck together because of the adhesive forces, such as van der Waals forces and ... [more ▼] Stiction is a major failure in microelectromechanical system (MEMS) devices in which two contacting surfaces can remain stuck together because of the adhesive forces, such as van der Waals forces and capillary forces. Stiction is a multiscale problem which is characterized by three different lengths: the MEMS device characteristic length, the roughness of the contacting surfaces, and the distance range of the adhesive forces. Because MEMS surfaces roughness and adhesive force distances are of comparable scales, the randomness in the contacting surfaces can result in important uncertainties on the interacting forces, and in turn lead to a scatter in the MEMS structural behavior. The purpose of this work is to quantify the uncertainties on the macro stiction behavior of a MEMS structure due to the randomness in its contacting surfaces. A full analysis, such as the combination of a Monte-Carlo simulation to generate random surfaces combined with finite element (FE) analyses to model the stiction behavior, is expensive in terms of the computational cost due to the difference in the scales between the macro characteristic length and the distance range of the adhesive forces. Thus, in this work, we develop a stochastic multiscale analysis. At the micro scale, the uncertainties in the interacting forces between two rough surfaces are investigated. The power spectral density function of the surface is characterized from experimental topology measurements, and interacting surfaces are then generated as Gaussian random surfaces. For each generated random surface, the interacting adhesive forces are calculated by using a modified Dejarguin-Muller-Toporov (DMT) model. The resulting adhesive contact forces can be integrated using the finite element method at the structural scale by associating to each discretized contacting point a sampled surface. We then use the Monte-Carlo method to quantify the uncertainties in the stiction behavior of the MEMS device. [less ▲] Detailed reference viewed: 49 (17 ULg)Propagation of uncertainties using probabilistic multi-scale models Lucas, Vincent ; Wu, Ling ; et al Conference (2015, February 25) When applying a multiscale approach, the material behavior at the macro-scale can be obtained from an homogenization scheme. To this end, at each integration-point of the macro-structure, the macrostress ... [more ▼] When applying a multiscale approach, the material behavior at the macro-scale can be obtained from an homogenization scheme. To this end, at each integration-point of the macro-structure, the macrostress tensor is related to the macro-strain tensor through the resolution of a micro-scale boundary value problem. At the micro-level, the macro-point is viewed as the center of a Representative Volume Element (RVE). However, to be representative, the micro-volume-element should have a size much bigger than the micro-structure size. When considering structures of reduced sizes, such as micro-electro-mechanical systems (MEMS), as the size of the devices is only one or two orders of magnitude higher than the size of their microstructure, i.e. their grain size, the structural properties exhibit a scatter at the macro-scale. The representativity of the micro-scale volume element is lost and Statistical Volume Elements (SVE) should be considered in order to account for the micro-structural uncertainties. These uncertainties should then be propagated to the macro-scale in order to predict the device properties in a probabilistic way. In this work we propose a non-deterministic multi-scale approach [1] for poly-silicon MEMS resonators. A set of SVEs is first generated under the form of Voronoi tessellations with a random orientation assigned for each silicon grain of each SVE. The resolution of each micro-scale boundary problem is performed by recourse to the computational homogenization framework, e.g. [2], leading to meso-scale material properties under the form of a linear material tensor for each SVE. Applying a Monte-Carlo procedure allows a distribution of this material tensor to be determined at the meso-scale. The correlation between the meso-scale material tensors of two SVEs separated by a given distance can also be evaluated. A generator of the meso-scale material tensor is then implemented using the spectral method [3]. The generator [1] accounts for a lower bound [4] of the meso-scale material tensor in order to ensure the existence of the second-order moment of the Frobenius norm of the tensor inverse [5]. A macro-scale finite element model of the beam resonator can now be achieved using regular finite-element, i.e. not conforming with the grains, and the material tensor at each Gauss point is obtained using the meso-scale generator, which accounts for the spatial correlation. A Monte-Carlo method is then used at the macro-scale to predict the probabilistic behavior of the MEMS resonator. As an example the beam resonator illustrated in Fig. 1(a) is made of poly-silicon, and 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 to be computed as illustrated in Fig. 1(b). However this methodology is computationally expensive due to the number of degrees of freedom required to study one sample. The proposed non-deterministic multi-scale strategy allows reducing this computational cost as the Monte-Carlo processes are applied on much smaller finite-element models. The method can also be applied in the context of fracture of thin poly-silicon film [6]. In this case, a set of meso-scopic cohesive laws can be obtained at the meso-scale from the resolution of different SVEs. The meso-scopic cohesive laws are obtained for each RVE from the finite element resolution of the Voronoi tessellations using the method proposed in [7]. The resulting statistical values for the critical energy release rate and for the critical strength can then be used for macro-scale simulations. [less ▲] Detailed reference viewed: 104 (11 ULg)Prediction of meso-scale mechanical properties of poly-silicon materials Lucas, Vincent ; Wu, Ling ; Arnst, Maarten et al Conference (2014, August 27) The miniature sizes of micro–electro–mechanical systems (MEMS) as well as the nature of their manufacturing processes, such as etching, material layer deposition, or embossing, are responsible for the ... [more ▼] The miniature sizes of micro–electro–mechanical systems (MEMS) as well as the nature of their manufacturing processes, such as etching, material layer deposition, or embossing, are responsible for the existence of a scatter in the final dimensions, material properties ... of manufactured micro–sensors. This scatter is potentially threatening the behavior and reliability of samples from a batch fabrication process, motivating the development of non-deterministic computational approaches to predict the MEMS properties. In this work we extract the meso-scale properties of the poly-silicon material under the form of a probabilistic distribution. To this end, Statistical Volume Elements (SVE) of the micro-structure are generated under the form of a Voronoï tessellation with a random orientation for each silicon grain. Hence, a Monte-Carlo procedure combined with a homogenization technique allows a distribution of the material tensor at the meso-scale to be estimated. As the finite element method is used to discretize the SVE and to solve the micro-scale boundary value problem, the homogenization technique used to extract the material tensor relies on the computational homogenization theory. In a future work, we will investigate, in the context of MEMS vibrometers, the propagation to the macro–scale of the meso-scale distribution of the homogenized elasticity tensor, with the final aim of predicting the uncertainty on their resonance frequencies. [less ▲] Detailed reference viewed: 72 (23 ULg)Prediction of macroscopic mechanical properties of a polycrystalline microbeam subjected to material uncertainties Lucas, Vincent ; Wu, Ling ; Arnst, Maarten et al in Cunha, Álvaro; Caetano, Elsa; Ribeiro, Pedro (Eds.) et al Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 (2014, June) The first resonance frequency is a key performance characteristic of MEMS vibrometers. In batch fabrication, this first resonance frequency can exhibit scatter owing to various sources of manufacturing ... [more ▼] The first resonance frequency is a key performance characteristic of MEMS vibrometers. In batch fabrication, this first resonance frequency can exhibit scatter owing to various sources of manufacturing variability involved in the fabrication process. The aim of this work is to develop a stochastic multiscale model for predicting the first resonance frequency of MEMS microbeams constituted of polycrystals while accounting for the uncertainties in the microstructure due to the grain orientations. At the finest scale, we model the microstructure of polycrystaline materials using a random Voronoï 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 second scale of interest, the meso-scale. In the future, using a stochastic finite element method, we will propagate these meso-scale uncertainties to the first resonance frequency at the coarser scale. [less ▲] Detailed reference viewed: 117 (45 ULg)Probabilistic model for MEMS micro-beam resonance frequency made of polycrystalline linear anisotropic material Lucas, Vincent ; Wu, Ling ; Arnst, Maarten et al Conference (2013, December) In order to ensure the accuracy of MEMS vibrometers, the first resonance frequency should be predicted at the design phase. However, this prediction cannot be deterministic: there is a scatter in the ... [more ▼] In order to ensure the accuracy of MEMS vibrometers, the first resonance frequency should be predicted at the design phase. However, this prediction cannot be deterministic: 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 and to propagate them up to the micro-beam resonance frequency. The objective is a non-deterministic model that can be used since the design stage. Towards this end a 3-scales stochastic model predicting the resonance frequency of a micro-beam made of a polycrystalline linear anisotropic material is described. Uncertainties are related to the sizes and orientations of the grains. The first part of the problem is a homogenization procedure performed on a volume which is not representative, due to the small scale of the problem inherent in MEMS. The method is thus non-deterministic and a meso-scale probabilistic elasticity tensor is predicted. This stage is followed by a perturbation stochastic finite element procedure to propagate the meso-scale uncertainties to the macro-scale, leading to a probabilistic model of the resonance frequency of the MEMS. [less ▲] Detailed reference viewed: 103 (33 ULg)Vérification expérimentale de modèles opto-thermo-élastiques simulés avec le logiciel OOFELIE Multiphysics Mazzoli, Alexandra ; ; Orban, Anne et al in 12ème colloque international francophone sur les Méthodes et Techniques Optiques pour l'Industrie (2011, November) Detailed reference viewed: 43 (8 ULg)Modeling and finite element analysis of mechanical behavior of flexible MEMS components Pustan, Marius ; ; et al in Microsystem Technologies (2011), 17(4), 553-562 This paper describes the studies of the mechanical characteristics of flexible MEMS components including theoretical approaches, finite element analysis and experimental investigations. Modeling and ... [more ▼] This paper describes the studies of the mechanical characteristics of flexible MEMS components including theoretical approaches, finite element analysis and experimental investigations. Modeling and finite element analyses together with theoretical and experimental investigations are performed to estimate the elastic behavior of MEMS components as microcantilevers, microbridges and micromembranes. Finite element analysis of microcomponents deflections under different loading and the stress distribution in beams are determined and compared with the experimental measurements performed using an atomic force microscope. The modeling of a micromembrane supported by four hinges that enable out-of-plane motion is presented. Finite element analysis and experimental investigations are performed to visualize the deflection of the mobile part of the micromembrane under an applied force and the stress distribution in hinges. In additional, this paper provides analytical relations to compute the stiffness and the stress of the investigated flexible MEMS components. [less ▲] Detailed reference viewed: 36 (7 ULg)Effects of the electrode positions on the dynamical behaviour of electrostatically actuated MEMS resonators Pustan, Marius ; ; et al (2011, April 18) The influence of the lower electrode positions on the dynamic response of polysilicon MEMS resonators is studied and presented in this paper. The change in the frequency response of investigated MEMS ... [more ▼] The influence of the lower electrode positions on the dynamic response of polysilicon MEMS resonators is studied and presented in this paper. The change in the frequency response of investigated MEMS resonators as function of the lower electrode positions is measured using a vibrometer analyzer. The decrease in the amplitude and velocity of oscillations if the lower electrode is moved from the beam free-end toward to the beam anchor is experimental monitored. The measurements are performed in ambient conditions in order to characterize the forced-response Q-factor of samples. A decrease of the Q- factor if the lower electrode is moved toward to the beam anchor is experimental determined. Different responses of MEMS resonators may be obtained if the position of the lower electrode is modified. Indeed the resonator stiffness, velocity and amplitude of oscillations are changed. [less ▲] Detailed reference viewed: 39 (5 ULg)Experimental validation of opto-thermo-elastic modeling in OOFELIE Multiphysics Mazzoli, Alexandra ; ; Orban, Anne et al in SPIE, Optical Systems Design (Marseille 5-8 septembre 2011) (2011) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 112 (11 ULg)Modeling and Finite Element Analysis of Mechanical Behavior of Flexible MEMS Components Pustan, Marius ; ; Rochus, Véronique et al in Courtois, Bernard (Ed.) DTIP 2010 (2010, May 05) This paper describes the studies of the mechanical characteristics of flexible MEMS components including theoretical approach, finite element analysis and experimental investigations. Modeling and finite ... [more ▼] This paper describes the studies of the mechanical characteristics of flexible MEMS components including theoretical approach, finite element analysis and experimental investigations. Modeling and finite element analyses together with theoretical and experimental investigations are performed to estimate the mechanical behaviour of MEMS components as microcantilevers, microbridges and micromembranes. The finite element analysis of microcomponents deflections under different loading and the stress distribution in beams is determined and compared with the experimental measurements performed using atomic force microscope. The modeling of a micromembrane supported by four hinges that enable out-of-plane and in-plane motions is presented. Finite element analysis and experimental investigations are performed to estimate the deflection of the mobile plate of the micromembrane under an applied force and to visualize the distribution of the stress in hinges. In additional, this paper provides analytical relations for stiffness and stresses of the investigated flexible MEMS components. [less ▲] Detailed reference viewed: 38 (8 ULg)Modeling of the fabrication and operation of 3-D self-assembled SOI MEMS ; ; et al (2006) Detailed reference viewed: 15 (0 ULg) |
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