Les procédés par infusion de résine consistant à infuser une résine liquide à travers un empilement de préformes fibreuses sous l’action d’une pression extérieure ap-pliquée à cet empilement. Un drainant peut être utilisé pour créer un lit de résine sur ou sous cet empilement fibreux. Ces procédés sont utilisés pour fabriquer des pièces minces utilisées dans l’aéronautique par exemple. Les caractéristiques physiques et mécaniques des pièces obtenues sont difficiles à prévoir et à contrôler. La simulation numérique peut donc aider à la maîtrise de ces procédés. Dans ce travail, un modèle numérique éléments finis est proposé pour simuler les procédés par infusion de résine. L’écoulement de la résine, considérée comme un fluide Newtonien incompressible, est décrit par les équations de Stokes dans le drainant (milieu très perméable), et par les équations de Darcy dans les préformes fibreuses (milieu faiblement perméable). Ce couplage Stokes - Darcyest réalisé par une approche monolithique, consistant à utiliser un seul maillage pour les deux milieux. La formulation mixte en vitesse - pression, est alors discrétisée par des éléments finis linéaire - linéaire, et stabilisée par une méthode multiéchelle dite "ASGS". L’interface entre Stokes et Darcy et le front de la résine sont chacun représentés par une fonction "Level-Set", et des conditions de couplage sont imposées sur l’interface qui sépare les deux milieux. Au cours du procédé, les préformes subissent de grandes déformations, que ce soit durant la phase de compaction, ou durant l’infusion de la résine. La pression de la résine fait alors gonfler les préformes. Les déformations des préformes sont traitées par une formulation Lagrangienne réactualisée établie en grandes déformations. Les préformes sèches ont un comportement élastique non linéaire, donné dans le sens transverse par l’expérience. L’effet de la résine sur les préformes humides est représenté par le modèle de Terzaghi. Lorsque les préformes se déforment, leur porosité et donc la perméabilité du milieu varient, affectant ainsi l’écoulement. La formule de Carman-Kozeny est utilisée pour relier porosité et perméabilité. Après avoir validé le couplage Stokes - Darcy par de nombreux cas tests et par la méthode des solutions manufacturées, diverses simulations 2D et 3D de procédés par infusion de résine sont présentées, incluant la déformation des préformes. Des comparaisons sont finalement faites avec succès entre simulation numérique et résultats expérimentaux dans un cas de géométrie simple. Des extensions à des cas tridimensionnels présentant des courbures et des variations d’inertie sont proposées en guise de perspectives. / Resin infusion-based processes are good candidates for manufacturing thin composite materials parts such as those used in aeronautics for instance. These processes consist in infusing a liquid resin into a stacking of fibrous preforms under the action of a mechanical pressure field applied onto this stacking where a stiff- distribution medium is also placed to create a resin feeding. Both physical and mechanical properties of the final pieces are rather difficult to predict and control. Numerical simulation are perfectly suited to master these processes. In the present work a numerical finite element modeling framework is proposed to simulate infusion processes. The flow of the assumed Newtonian resin is described in the distribution medium, a highly porous medium, through Stokes’ equations and through Darcy’s equations in the fibrous preforms, very low permeability media. This coupled Stokes-Darcy flow is modeled in a monolithic approach which consists in using a single mesh for both media. The mixed velocity- pressure formulation is then discretized by linear-linear finite elements, stabilized by a so-called ASGS multi-scale approach. Both Stokes-Darcy interface and fluid front are represented individually thanks to "Level-Set" functions, and some specific coupling conditions are prescribed on the interface separating both fluid and porous media. During the process, orthotropic preforms undergo finite strains, either during the compaction stage when resin is not yet present, or during resin infusion. Resin pressure then tends to make the preforms swell. Preforms deformations are represented through an updated Lagrangian formulation for finite deformations. Dry preforms possess a non-linear elastic behaviour in their transverse direction - across their thickness- given by existing experimental measurements. The effect of the presence of resin in the wet preforms is accounted for using a Terzaghi’s equivalent model. Also, when preforms deform their porosity will change, and so will their permeability, modifying the resin flow. A Carman-Kozeny model is then used to relate porosity and permeability. After the Stokes-Darcy coupling is validated both on numerous tests cases and using the method of manufactured solutions, various 2D and 3D simulations of injection and infusion-based processes are analyzed.The latter includ- ing preform deformations along with resin flow. Comparisons with existing experimental measurements permit to validate the approach on a simple geometry. Last, some ex- tensions to more complex 3D cases are proposed as outlooks, including curvatures and thickness variations.

Dans cette thèse, nous nous intéressons à la simulation numérique d'écoulements instationnaires de deux fluides visqueux non miscibles, séparés par une interface mobile. Plus particulièrement des écoulements sans choc constitués d'une phase gazeuse et d'une phase liquide sont considérés. Pour modéliser de tels écoulements, une approche dans laquelle le gaz est décrit par les équations de Navier-Stokes compressible et le liquide par les équations de Navier-Stokes incompressible est proposée. C'est le couplage de ces deux modèles qui constitue l'originalité et l'enjeu principal de de cette thèse. Pour traiter cette difficulté majeure, une méthode globale (i.e. la même dans chaque phase) et simple à mettre en oeuvre est élaborée. L'utilisation des équations de Navier-Stokes formulées de façon unifiée pour les inconnues primitives (pression, vitesse et température) constitue le point de départ pour la construction de notre méthode qui repose sur les composants suivants: une méthode d'éléments finis stabilisés pour la discrétisation spatiale des équations de Navier-Stokes; une approche Level Set pour représenter précisément l'interface dont l'équation de transport a été résolue par une méthode de type Galerkin Discontinu; et des grandeurs moyennes pour traiter les discontinuités à l'interface. Le bon comportement de notre approche est illustré sur différents tests mono et bi-dimensionnels. / In this work, we are interested in the numerical simulation of instationnary viscous flows of two immiscible fluids, separated by a mobile interface. In particular, flows without shock composed of a gas phase and a liquid phase are considered. In order to modelize such flows, an approach in which the gaz is described by compressible Navier-Stokes equations and the liquid by incompressible Navier-Stokes équations is proposed. The coupling between these two models is the originality and the stake of this thesis. To treat this important difficulty, a global (i.e. the same for each phase) and simple method is elaborated. In our procedure we propose, using the Navier-Stokes equations formulated in set of primitives unknowns (pressure, velocity and temperature), to elaborate a strategy that relies on the follow components: the stabilized finite element method to discretize spatially the Navier-Stokes equations; the Level Set method for tracking the interface precisely with a discontinuous Galerkin method to solve the associated transport equation; and some averaged quantities to treat the discontinuities at the interface. The good behaviour of this approach is performed on both one and two spatial dimensions.

<p>The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.</p><p>We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode. </p><p>We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.</p><p>The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.</p><p>Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.</p><p>The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.</p> / Dissertation

Level set method is a boundary tracking method that uses an implicit function to define the boundary location. By using the implicit function to define the structural boundary the level set method can be used for topology optimisation. The level set method has previously been used to solve a range of structural optimisation problems. The aim of this thesis is to extend the application of the level set method to additional applications of structural optimisation. A robust method of 3D level set topology optimisation is developed and tested. The use of a hole insertion method was found to be advantageous, but not vital, for 3D level set topology optimisation. The level set method is used to optimise the internal structure of a proximal femur. Similarities between the optimal structure and real internal trabecular bone architecture suggest that the internal bone structure may be mechanically optimal. Stress constrained level set topology optimisation is performed in 2D. Stress shape sensitivities are derived and interpolated to obtain smooth boundary sensitivity, resulting in feasible stress constrained solution in numerical examples. A new generic objective hole insertion method is used to reduce dependence on the initial solution. A level set method for optimising the design of fibre angles in composite structures is also introduced. Fibre paths are implicitly defined using the level set function. Sensitivity analysis is used to update the level set function values and optimise the fibre path. The method implicitly ensures continuous fibre paths in the optimum solution, that could be manufactured using advanced fibre placement.

The process industry is concerned with the processing of crude resources into other products. Such crudes consist of multiphase components that introduce major challenges to the operators; hence the need for efficient instrumentations that address such challenges is highly desirable. One major need is an early deposit detection system that detects deposit before it builds-up in a pipeline or equipment to prevent any possible hazard. Another critical requirement is the need to continuously monitor the flow and deduce the flow rate of every individual phase in order to study and analyse the produced product. Hence, in order to ensure safety, increase profits, optimize production and ensure production quality, the multiphase flow must be adequately monitored and controlled. This thesis demonstrated the efficiency of novel ECT algorithms for early deposit detection and multiphase flow measurement in order to measure the flow rate of all separate phases. This thesis focuses on developments in ECT image reconstruction specifically the inverse solutions and is divided into three main studies where they all build up to complete each other. In the first study, ECT is used for the first time with a narrowband pass filter to focus on targeted locations in a pipe where dielectric contaminants are expected to deposit in order to enhance the resolution of the produced images. The experimental results showed that different deposit regimes and accumulated fine deposits could be detected with high resolution. The second study allowed a better understanding of how conductive material could be imaged using a conventional ECT device and how state of the art algorithms such as iterative total variation regularisation method and the level set method could enhance this application. Also, absolute ECT imaging is presented for the first time where the level set algorithm uses only one set of ECT measurement data. This study gives a novel solution for detecting conductive deposits as well as paves the way to use the new level set algorithm for multiphase flow measurement. In the third study, the novel narrowband level set algorithm was modified to image multiphase media in order to correctly determine the number, location and concentration of the present phases. The innovative absolute ECT imaging using level set method is tested with high contrast and low contrast multiphase data, which adds more to the challenge.

First of all, the PDE form of the classical level set function phi is parameterized with an analytical form of Radial Basis Function (RBF), which is real-valued and continuously differentiable. Such that the upwind scheme, extension velocity and reinitialization algorithms in solving the discrete Hamilton-Jacobi equation can be waived in the numerical process, the whole framework is transformed into a standard mathematical programming problem in which the linear objective function can be directly optimized by a gradient algorithm - shape sensitivity. The minimization of the mean compliance is studied and presented to demonstrate the advantages of the parametrical method. / Parametrization substantially reduces the complexity of the original discrete PDE level set method. However, the result shows that the high number of RBF knots leads to dense coefficient matrices. Thus, it induces numerical instabilities, slow convergence and less accuracy in the process. Consequently, we then study the distribution of knots density for faster computation. By updating the movement of the knot, the knot moves towards the position where the change is directly determined by the shape sensitivity. In such case, we may use lesser number of knots to describe the properties of the system while the smoothness of the implicit function is satisfied. The sensitivity study is evaluated carefully and discussed in detail. Results show a significant improvement in the computational speed and stability. / The study found significant improvement obtained in the structural optimization with the parametric level set method, both the stability and efficiency were given as the benefits of using the method of the parametrization. / Traditional structural optimization approaches can be referred to as sizing optimization, since their design variables are the proportions of the structure or material. A major restriction in the sizing problem is that the shape and the topology of the structure are fixed a priori. Undoubtedly, changes in shape (e.g., curved boundary) and topology (e.g., holes in a member) could produce more significant improvement in dynamic performance than modifications in size alone. A recent development of shape and topology optimization based on the implicit moving boundaries with the use of the renowned level set method is regarded as one of the most sophisticated methods in handling the change of the structural topology. In this thesis, we study the parametrization of the classical level set method for the structural optimization and the associated computational methodology. / Usually, a large-scale model will lead to bulk coefficient matrices in the RBF optimization and the linear function normally require O (N3) flops and O (N2) memory while processing. It is becoming impractical to solve as N goes over 10,000. In fact, the dense system equation matrix frequently leads to the numerical instabilities and the failure of the optimization. Finally, we introduce the method of Partition of Unity (POU) to deal with this problem. POU is often used in 3D reconstruction of implicit surfaces from scattered point sets. It breaks the global domain into smaller overlapping subdomains such that the implicit functions can be more efficiently interpolated. Meanwhile, the global solution is obtained by blending all the local solutions with a set of weighting functions. The algorithm of POU is presented here, and we analyze and discuss the numerical results accordingly. / Ho, Hon Shan. / Adviser: Michael Y. Wang. / Source: Dissertation Abstracts International, Volume: 73-03, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 106-119). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Research in the biomedical sciences is incredibly diverse and often involves the interaction of specialists in a variety of fields. In particular, quantitative, mathematical, and computational methods are increasingly playing significant roles in studying problems arising in biomedical science. This is particularly exciting for mathematical modeling as the complexity of biological systems poses new challenges to modelers and leads to interesting mathematical problems. On the other hand mathematical modeling can provide considerable insight to laboratory and clinical researchers. In this thesis we develop mathematical representations for three biological processes that are of current interest in biomedical science. A deeper understanding of these processes is desirable not only from the standpoint of basic science, but also because of the connections these processes have with certain diseases. The processes we consider are collective cell motility, bone remodeling, and injury response in articular cartilage. Our goals are to develop mathematical representations of these processes that can provide a conceptual framework for understanding the processes at a fundamental level, that make rigorous the intuition biological researchers have developed about these processes, and that help to translate theoretical and experimental work into information that can be used in clinical settings where the primary concern is in treating diseases associated with the process.

Cardiovascular modeling has the capability to provide valuable information allowing clinicians to better classify patients and aid in surgical planning. Modeling is advantageous for being non-invasive, and also allows for quantification of values not easily obtained from physical measurements. Hemodynamics are heavily dependent on vessel geometry, which varies greatly from patient to patient. For this reason, clinically relevant approaches must perform these simulations on patient-specific geometry. Geometry is acquired from various imaging modalities, including magnetic resonance imaging, computed tomography, and ultrasound. The typical approach for generating a computational model requires construction of a triangulated surface mesh for use with finite volume or finite element solvers. Surface mesh construction can result in a loss of anatomical features and often requires a skilled user to execute manual steps in 3rd party software. An alternative to this method is to use a Cartesian grid solver to conduct the fluid simulation. Cartesian grid solvers do not require a surface mesh. They can use the implicit geometry representation created during the image segmentation process, but they are constrained to a cuboidal domain. Since patient-specific geometry usually deviate from the orthogonal directions of a cuboidal domain, flow extensions are often implemented. Flow extensions are created via a skilled user and 3rd party software, rendering the Cartesian grid solver approach no more clinically useful than the triangulated surface mesh approach. This work presents an alternative to flow extensions by developing a method of applying vessel inlet and outlet boundary conditions to regions inside the Cartesian domain.

One outstanding challenge to understanding the behaviors of organisms and other complexities found in nature through the use of computational fluid dynamics simulations lies in the ability to accurately model the highly tortuous geometries and motions they generally exhibit. Descriptions must be created in a manner that is amenable to definition within some operative computational domain, while at the same time remaining fidelitous to the essence of what is desired to be understood. Typically models are created using functional approximations, so that complex objects are reduced to mathematically tractable representations. Such reductions can certainly lead to a great deal of insight, revealing trends by assigning parameterized motions and tracking their influence on a virtual surrounding environment. However, simplicity sometimes comes at the expense of fidelity; pared down to such a degree, simplified geometries evolving in prescribed fashions may fail to identify some of the essential physical mechanisms that make studying a system interesting to begin with. In this thesis, and alternative route to modeling complex geometries and behaviors is offered, basing its methodology on the coupling of image analysis and level set treatments. First a semi-Lagrangian method is explored, whereby images are utilized as a means for creating a set of surface points that describe a moving object. Later, points are dispensed with altogether, giving in the end a fully Eulerian representation of complex moving geometries that requires no surface meshing and that translates imaged objects directly to level sets without unnecessary tedium. The final framework outlined here represents a completely novel approach to modeling that combines image denoising, segmentation, optical flow, and morphing with level set- based embedded sharp interface methods to produce models that would be difficult to generate any other way.

This dissertation presents a study on the development of a numerical model aimed at simulating free surface flow, which still remains an active research area. Modeling these processes is very challenging since the interface between air and water is characterized by sharp discontinuities in fluid properties and flow characteristics due to different densities, viscosities, surface tension and consequent discontinuities in spatial gradients of velocity and pressure. The constraint of incompressibility poses another difficulty on the efficient design of algorithms. Recently, the level set method has emerged as a powerful tool for evolving interfaces in computational science and engineering for a wide range of applications while the finite element method has been long known for its geometrical flexibility. An effort to combine these two methods is made in this study. Several benchmark problems are used for the test of the developed code in view of temporal and spatial accuracy. Then, the capability and efficiency of the model are extended with advanced turbulence models and parallel algorithm. The model is applied to problems of practical importance in hydraulics, including hydraulic jump under a sluice gate and the design of spillways for fish migration. The main focus is on the capturing of free surface and identifying and understanding of the vortical structures and nonhydrostatic pressure distribution. The model has proved to be very effective for these purpose. The new technique dealing with air-water interface in a more physically accurate way is introduced for future development and the new method is applied to the problems of static equilibrium for validation.