Abstract Micro-electromechanical systems (MEMS) are subject to inevitable and inherent uncertainties in their dimensional and material parameters. Those lead to variability in their performance and reliability. Manufacturing processes leave substantial variability in the shape and geometry of the device due to its small dimensions and high feature complexity, while the material properties of a component are inherently subject to scattering. The effects of these variations have to be considered and a modeling methodology is needed in order to ensure required MEMS performance under uncertainties. Furthermore, in the design of high-Q micro-resonators, dissipation mechanisms may have detrimental effects on the quality factor (Q). One of the major dissipation phenomena to consider is thermoelastic damping, so that performances are directly related to the thermoelastic quality factor, which has to be predicted accurately. The purpose of this research is to develop a numerical method to analyze the effects of geometric and material property random variations on the thermoelastic quality factor of micro-resonators. The extension of the Perturbation Stochastic Finite Element Method (PSFEM) to the analysis of strongly coupled multiphysic phenomena allows the quantification of the influence of uncertainties, making available a new efficient numerical tool to MEMS designers. Résumé Dans le domaine des microsystèmes électromécaniques (MEMS), les micro-résonateurs jouent un rôle important pour le développement de micro-capteurs de plus en plus précis (ex : micro-accéléromètres). Dans cette optique daugmentation de la précision, les pertes dénergie qui limitent les performances des micro-résonateurs doivent être identifiées et quantifiées. Le facteur limitant des micro-résonateurs actuels est leur facteur de qualité thermo-élastique, qui doit donc être prédit de manière précise. De plus, suite à la tendance actuelle de miniaturisation et complexification accrues des MEMS, les sources de dispersions sont très nombreuses, à la fois sur les constantes physiques des matériaux utilisés et sur les paramètres géométriques. La mise au point doutils numériques permettant de prendre en compte les incertitudes de manière efficace est donc primordiale afin daméliorer les prestations densemble du microsystème et dassurer un certain niveau de robustesse et de fiabilité. Le but de cette recherche est de développer une méthode numérique pour analyser les effets des variations aléatoires des propriétés matérielles et géométriques sur le facteur de qualité thermo-élastique de micro-résonateurs. Pour ce faire, lapproche dite perturbative de la méthode des éléments finis stochastiques (PSFEM) est étendue à lanalyse de phénomènes multiphysiques fortement couplés, fournissant ainsi aux acteurs de lindustrie des MEMS un nouvel outil de conception efficace.

Modeling of the time-dependent behavior of cement paste has always been a difficulty. In the past, viscoelastic behavior of cementitious materials has been primarily attributed to the viscoelastic properties of C-S-H components. Recent experimental results show that C-S-H may not exhibit as much creep and relaxation as previously thought. This requires new consideration of different mechanisms leading to the viscoelastic behavior of cement paste. Thus the objective of this thesis is to build a computational model using finite element method to predict the viscoelastic behavior of cement paste, and using this model, virtual tests can be carried out to improve understanding of the mechanisms of viscoelastic behavior. The primary finding from this thesis is that the apparent viscoelastic behavior due to dissolution of load bearing phases is substantial. The dissolution process occurring during the hydration reaction can change the stress distribution inside cementitious materials, resulting in an apparent viscoelastic behavior of the whole cementitious materials. This finding requires new consideration of mechanisms of time-dependent behavior of cementitious materials regarding the dissolution process of cement paste.

Hydrocephalus is a clinical conditon where the brain tissue is deformed by the expanding ventricules. In this thesis, the mechanical deformation of a hydrocephalic brain is studied using a biomechanical model, where the material properties of the tissue are described by a viscoelastic model. A set of governing equations is derived when the motion is quasi-static motion and deformation is small. Then, finite element method is used for spatial discretization, and finite difference and trapezoidal rule are used for time-stepping. Moreover, the computational meshes are generated from medical images of patient's brain using level set method and a program called DistMesh. Numerical stability of the time-stepping scheme is also studied. <br /><br /> Several numerical studies are conducted to investigate several aspect of the brain with hydrocephalus. The state of stress of the tissue is found to be compressive everywhere in the brain. The viscoelastic properties of the brain are investigated and found to be dominated by elastic response. Lastly, the displacement made by the ventricular wall as it expands and shrinks is found to be non-uniform.

In this paper a continuous Galerkin multiscale method (CGMM) and a discontinuous Galerkin multiscale method (DGMM) are proposed, both based on the variational multiscale method for solving partial differential equations numerically. The solution is decoupled into a coarse and a fine scale contribution, where the fine-scale contribution is computed on patches with localized right hand side. Numerical experiments are presented where exponential decay of the error is observed when increasing the size of the patches for both CGMM and DGMM. DGMM gives much better accuracy when the same size of the patches are used.

Hydrocephalus is a clinical conditon where the brain tissue is deformed by the expanding ventricules. In this thesis, the mechanical deformation of a hydrocephalic brain is studied using a biomechanical model, where the material properties of the tissue are described by a viscoelastic model. A set of governing equations is derived when the motion is quasi-static motion and deformation is small. Then, finite element method is used for spatial discretization, and finite difference and trapezoidal rule are used for time-stepping. Moreover, the computational meshes are generated from medical images of patient's brain using level set method and a program called DistMesh. Numerical stability of the time-stepping scheme is also studied. <br /><br /> Several numerical studies are conducted to investigate several aspect of the brain with hydrocephalus. The state of stress of the tissue is found to be compressive everywhere in the brain. The viscoelastic properties of the brain are investigated and found to be dominated by elastic response. Lastly, the displacement made by the ventricular wall as it expands and shrinks is found to be non-uniform.

The purpose of this study is to analyze baseball collision by using finite element method, and investigate batting effect on the sweet spot on the bat and then change the baseball geometry parameter. In addition, the researcher would like to investigate the effect of flight on batted ball by changing swing parameter. LS-DYNA is used to simulate collision on the different position on the bat after using SolidWorks to build modal, then compare the results to locate the exact position of sweet spot on the bat. By building different weight, length and radius of bat barrel, and simulate collision individually, the researcher wishes to investigate the influence of changing bat geometry parameter to batting effect on sweet spot. At last changing the undercut distance and bat swing angle, two of the swing parameter, to simulate collision, and the results of collision are used to get flight trajectory by numerical method, then analyze the influence of changing swing parameter to batted ball range. This study can provide bat geometry characteristic, swing information, and a reference for choosing a baseball bat, even help adjust batting feel for the batter.

As part of a larger effort to understand the fundamental knowledge of polymer scratch behavior, this dissertation is focused on both experimental study and numerical analysis of scratch deformation of a broad range of polymers, with an emphasis on the mechanical understanding of how the scratch-induced damage is formed. An instrumented progressive load scratch method recommended by ASTM/ISO standards was adopted for the experimental work. The commercial finite element (FE) method package ABAQUS was employed as a numerical simulation tool to describe the stress-strain fields, and it analyzes the deformation mechanisms during the scratch process. A thorough parametric study has been performed to assess the influence of material parameters and surface properties, such as Young's modulus, yield strength, and friction coefficient, on the polymer scratch behavior. Upon investigation of the scratch behaviors of a broad range of polymer materials, various kinds of scratch damage features are identified and correlated with the mechanical characteristics of the polymers. A generalized scratch damage mechanism map for polymers is presented. Correlation between different material types and scratch damage mechanisms is made. It is found that both the material characteristics and the stress state exerted on the scratched surface are responsible for the observed scratch damage mechanisms. The phenomenological deduction of the scratch damage process based on the stick-slip mechanism is established. A more realistic material law for the scratch analysis is also provided. To evaluate the polymer resistance against scratch visibility quantitatively, an entirely new automated on-set scratch visibility determination methodology is developed based on typical visual characteristics of human eyes. Its application on the evaluation of mar and abrasion of polymer is also explored. This new methodology can quantify polymer scratch resistance consistently and reliably regardless of the sample surface characteristics and color.

The purpose of this study is to investigate the function of the different structural designs of golf club head models (including a deep head, a shallow back, and a shallow head) and to get the optimum golf club head through the software simulation. By means of software SolidWorks, the researcher draws three main club head models. The C ++ was used for a linear programming to control the golf club head thickness including an impact face, a crown, a sole, a toe and a heel under the definite weight. The simulation also helps adjust the center of gravity position of the golf club head and integrates with the finite element method software LS_Dyna in analyzing the impact procedure between the golf club head and the golf ball. In addition, the researcher preceded the analysis by replacing the crown surface as carbon fiber reinforcement polymers (CFRP). He also investigated the off-centered hit effects through the impact analysis. It is expected that study findings can be extracted. Through the simulation of the hit effects, the golf club head designers will be inspired to create more effective golf club heads.

Abstract Accompany a rapid growth in the semiconductor industry in the past few year, most components gradually used the small dimension as its basic structures. Due to the reduction of component size will induces highly concentrated on circuit and dimension, it also incurs a lots problem, such as electromagnetic interference, high temperature and thermal stress, which will decrease the product reliability. The most common damage in the semiconductor product is thermal fatigue, which is caused by thermal stress concentrated under repeatedly temperature variation loading. Usually, the thermal cycle loading is applied to induce the fatigue destruction and predict the product reliability, but this method spends one cycle for 80min which is time-consumption. Therefore, in this thesis, the finite element method package is used to simulate and evaluate the plastic variation of solder bump and the relation between different temperatures loading and equivalent plastic strain under different temperature range test. Through the Coffin-Manson equation, the equivalent plastic strain can be used to predict the fatigue live, which can be precisely accelerating the fatigue test.

The current packaging trend toward to smaller and thinner has pushed the manufacturing technology to the limits. During the assembly processes of IC packages, delamination at interfaces and mechanical breakage of components are common mode of failure. The induced thermal stress within the package is one of the major contributions to these failures. According to the disparity of the coefficient of thermal expansion (CTE) between different components, internal thermal stress and warpage will be induced when the package undergoes temperature excursion. In this paper, the Die attach epoxy curing and encapsulation curing process induced warpage and thermal stress were studied by finite element software Marc & Mentat. As comparison, two kinds of Molding materials of the package considered, and the result will compared with the experimental data. Finally, studied the effect of the material thickness and the impact significance of each design variable on the design objective will also be discussed.