The issue of accurately determining the effective properties of composite materials has received the attention of numerous researchers in the last few decades and continues to be in the forefront of material research. Micromechanics models have been proven to be very useful tools for design and analysis of composite materials. In the present work, a versatile micromechanics modeling framework, namely, the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH), has been invented and various micromechancis models have been constructed in light of this novel framework. Considering the periodicity as a small parameter, we can formulate the variational statements of the unit cell through an asymptotic expansion of the energy functional. It is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories (MHT) can be reproduced from this variational statement. Finally, we employed the finite element method to solve the numerical solution of the constrained minimization problem. If the local fields within the unit cell are of interest, the proposed models can also accurately recover those fields based on the global behavior. In comparison to other existing models, the advantages of VAMUCH are: (1) it invokes only two essential assumptions within the concept of micromechanics for heterogeneous material with identifiable unit cells; (2) it has an inherent variational nature and its numerical implementation is shown to be straightforward; (3) it calculates the different material properties in different directions simultaneously, which is more efficient than those approaches requiring multiple runs under different loading conditions; and (4) it calculates the effective properties and the local fields directly with the same accuracy as the fluctuation functions. No postprocessing calculations such as stress averaging and strain averaging are needed. The present theory is implemented in the computer program VAMUCH, a versatile engineering code for the homogenization of heterogeneous materials. This new micromechanics modeling approach has been successfully applied to predict the effective properties of composite materials including elastic properties, coefficients of thermal expansion, and specific heat and the effective properties of piezoelectric and electro-magneto-elastic composites. This approach has also been extended to the prediction of the nonlinear response of multiphase composites. Numerous examples have been utilized to clearly demonstrate its application and accuracy as a general-purpose micromechanical analysis tool.

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Porous ceramics and porous ceramic composites are emerging functional materials that have found numerous industrial applications, especially in energy conversion processes. They are characterized by random microstructure and high porosity. Examples are ceramic candle filters used in coal-fired power plants, gas-fired infrared burners, anode and cathode materials of solid oxide fuel cells, etc. In this research, both experimental and theoretical work have been conducted to characterize and to model the mechanical behavior and durability of this novel class of functional material. Extensive experiments were performed on a hot gas candle filter material provided by the McDermott Technologies Inc (MTI). Models at micro-/meso-/macro- geometric scales were established to model the porous ceramic material and fiber reinforced porous ceramic material. The effective mechanical properties are of great technical interest in many applications. Based on the average field formalism, a computational micromechanics approach was developed to estimate the effective elastic properties of a highly porous material with random microstructure. A meso-level analytical model based on the energy principles was developed to estimate the global elastic properties of the MTI filament-wound ceramic composite tube. To deal with complex geometry, a finite element scheme was developed for porous material with strong fiber reinforcements. Some of the model-predicted elastic properties were compared with experimental values. The long-term performance of ceramic composite hot gas candle filter materials was discussed. Built upon the stress analysis models, a coupled damage mechanics and finite element approach was presented to assess the durability and to predict the service life of the porous ceramic composite candle filter material. / Ph. D.

Part I (Efficient Endochronic Finite Element Analysis: an Example of a Cyclically Loaded Boron/Aluminum Composite): A convenient and efficient algorithmic tangent matrix approach has been developed for 3-D finite element (FE) analysis using the endochronic theory without a yield surface. The underlying algorithm for integrating the endochronic constitutive equation was derived by piecewise linearization of the plastic strain path. The approach was employed to solve a micromechanics boundary value problem of a cyclically loaded unidirectional boron/6061 aluminum composite. All the FE results consistently demonstrate superior numerical stability and efficiency of the proposed method. Extensions of the method to endochronic plasticity with a yield surface and to the plane stress case are also presented. Part II (Simple and Unified Finite Element Formulation for Doubly Periodic Models: Applications to Boron/Aluminum Composites): A simple and unified weak formulation and its convenient FE implementation have been proposed. The weak formulation is valid for any doubly periodic model under uniform 3-D macro-stress, and serves as a common rational foundation of different FE approaches. The algorithmic tangent matrix approach for the endochronic theory has been incorporated into the FE formulation to model isothermal, rate-independent plastic macro-deformation of unidirectional fibrous composites with idealized two-phase micro-structure and backed-out inelastic matrix properties. Methods for determining inelastic material parameters of the matrix have been established. Numerical results for a B/6061 AI composite subjected to on-axis and off-axis monotonic tensile loadings are in good agreement with experimental data. The micromechanics model also shows the potential for quantitative characterization of complicated cyclic behavior. Finally, some effects of model geometry on overall plastic response of the B/6061 AI composite are discussed from the viewpoint of theoretical-experimental correlation. / Ph. D.

One of the key issues concerning the durability of composites is the strength and stiffness degradation during service. Traditionally, these materials have been analyzed by methods which do not take into account variations in the material at the fiber/matrix level. In addition, manufacturing techniques have advanced enough so that composites can be designed from the fiber/matrix level up. As a result, it is important to predict the effect microlevel variations in the material have on macroscopic behavior. Therefore, it is vital to use a micromechanics model to calculate stress and displacement variations. In this study, the strength and stiffness of polymer matrix composites will be determined. To accomplish this, a variational model which calculates microstresses and strains due to damage is used in conjunction with a statistical strength model to predict strength. The results are compared to experimental results of uniaxial strength of carbon fiber composites. In addition, the stiffness of a continuous fiber composite was predicted and compared to a rule of mixtures equation of stiffness. A comparison showed very good agreement. To study the effect of damage, the stiffness of a continuous fiber composite with fiber fragmentation is predicted as a function of fragmentation length and fiber volume fraction. Finally the stiffness of a short-fiber composite is predicted and compared to analytical and experimental results. / Master of Science

This thesis presents the design of multifunctional structures through the optimal placement of nanomaterial additives. Varying the concentration of Carbon Nanotubes (CNTs) in a polymer matrix affects its local effective properties, including mechanical stiffness, electrical conductivity, and piezoresistivity. These local properties in turn drive global multifunctional performance objectives. A topology optimization algorithm determines the optimal distribution of CNTs within an epoxy matrix in an effort to design a set of structures that are capable of performing some combination of mechanical, electrical, or peizoresistive functions. A Pareto-Based Restart Method is introduced and may be used within a multi-start gradient based optimization to obtain well defined multiobjective Pareto Fronts. A linear design variable filter is used to limit the influence of checkerboarding. The algorithm is presented and applied to the design of beam cross-sections and 2D plane stress structures. It is shown that tailoring the location of even a small amount of CNT (as low as 2 percent and as high as 10 percent, by volume) can have significant impact on stiffness, electrical conductivity, and strain-sensing performance. Stiffness is maximized by placing high concentrations of CNT in locations that either maximize the bending rigidity or minimize stress concentrations. Electrical conductivity is maximized by the formation of highly conductive paths between electrodes. Strain-sensing is maximized via location of percolation volume fractions of CNTs in high strain areas, manipulation of the strain field to increase the strain magnitude in these areas, and by avoiding negative contributions of piezoresistivity from areas with differing net signed strains. It is shown that the location of the electrodes can affect sensing performance. A surrogate model for simultaneous optimization of electrode and topology is introduced and used to optimize a 2D plane stress structure. This results in a significant increase in sensing performance when compared to the fixed-electrode topology optimization. / Ph. D. / This dissertation presents a method that allows for the best placement of a limited amount of filler material within a base matrix material to form an optimal composite structure. Adding filler material, in this case Carbon Nanotubes, can change the effective behavior of the composite structure, enhancing the capabilities of the base matrix material by adding structural stiffness, electrical conductivity, and even the ability for the structure to measure its own strains. The degree to which these changes occur is dependent on the amount of filler material present in any given subsection of the structure. The method then is focused on determining how much of the filler to place in different subsections of the structure to maximize several measures of performance. These measures pertain to structural performance, electrical conductivity, and the structure’s ability to sense strains. Steps are taken within the method to remove non-physical designs and also to find the overall best design, called the global minima. The method is applied to several test structures of varying complexity, and it is shown that the optimization method can heavily influence performance by tailoring the filler material distribution. Further electrical and sensing performance gains can be obtained by properly selecting where the electrodes are located on the structure. This is demonstrated by including electrode placement in the design method along with the filler distribution.

As climate change escalates and the demands for energy resources increase, modern geotechnical engineering must tackle critical challenges to ensure sustainable development and enhance the resilience of infrastructure in society. The coupled chemo-hydro-mechanical processes in multiphase materials present significant challenges in geotechnical engineering, particularly for applications like carbon sequestration, geological disposal of nuclear waste, and hydraulic fracturing with reactive fluids, all of which involve highly heterogeneous and strongly anisotropic multiphysics environments. This dissertation introduces a multiphysical computational framework specifically designed to address the challenges associated with these unconventional applications. In this dissertation, we consider not only the local multiphysical coupling effects in the constitutive model but also the nonlocal effects arising from pore fluid flow, chemical species convection and diffusion, chemical reactions occurring in both solid and fluid constituents, and damage due to fluid pressure acting on fractures in the solid. We have integrated all these physical processes and developed a single unified model capable of handling the complex hydro-chemo-mechanical responses of geomaterials under varying geochemical conditions, confining pressures, and external loading scenarios. This computational framework offers a comprehensive simulation tool to investigate the long-term stability of geomaterials, which is determined by the intensity of chemical reactions under specific temperature and pressure conditions (assuming an isothermal condition in this dissertation), as well as the sustainability of geotechnical infrastructure in erosive environments driven by both mechanical and chemical processes. Three key aspects of engineering applications related to the effects of chemical reactions in geotechnical engineering are addressed. Firstly, we have integrated a complete calcite reaction system into poromechanics to couple pore geochemistry with poroelasticity theory. This integration is capable of predicting the geomechanical response essential for long-term stability analysis in \ch{CO2} sequestration engineering. Key features of this model include a multi-field finite element approach, local-equilibrium explicit geochemistry characterization of the calcite dissolution/precipitation reaction system, a robust algorithm for sequentially coupling pore geochemistry with poromechanics, and strategies to enhance the computational efficiency of solvers. Secondly, for applications involving acid working fluids in hydraulic fracturing, we have extended and adapted previous models within the phase field method framework. This extended integration effectively addresses the effects of chemically assisted fracturing in hydraulic fracturing operations. The key innovations of this model are the implementation of the phase field method to capture crack behaviors with poromechanics, the modeling of acid fluid transport in porous media and fractures, and its application to multiple mineral reaction systems. Thirdly, we have proposed a constitutive model that incorporates pore geochemistry and the pressure dissolution effect into internal variables, effectively capturing the chemical reactions contributing to softening in geomaterials. This model effectively illustrates and predicts chemically induced weathering or damage in granular porous media, such as sinkholes and subsidence. Derivations of a thermodynamically-based degradation index consider the influences of pore geochemistry and contact forces between grains and bonds. The model also proposes cross-scale relationships that consider reaction effects from individual particle sizes to particle aggregates. Furthermore, these relationships are incorporated into classical Cam-Clay-type models, along with the derivation of a consistent tangent modulus. / Dissertation / Doctor of Philosophy (PhD) / This thesis presents the comprehensive behaviors of geomaterials under mechanical, fluid, and chemical interactions, which result in displacement and cracking. Since there is no existing software or simulation tool that includes all the physical behaviors considered in this dissertation, the development and implementation of these physical mechanisms, followed by testing and analysis for engineering problems, constitutes the main contribution of this work. The newly developed simulation tool ranges from simulating the mechanical behavior of porous media saturated with water and reactive fluid to modeling the seepage of water/reactive fluid that triggers damage (cracks) in the porous media. This simulation tool can effectively analyze engineering problems that focus on the interactions between the working fluid and the host solid matrix under complex solution conditions. Examples include modeling carbon sequestration in saline aquifers and the storage of nuclear waste in subsurface repositories etc. The simulation tool proposed in this thesis incorporates rigorous mathematical derivations, efficient and accurate multiscale discretization techniques, robust non-iterative and iterative numerical coupling strategies, and thorough comparisons between numerical results and experimental/laboratory data. Simultaneously, it is important to recognize the model's limitations. Although the model assumes local equilibrium and interactions between physical mechanisms, it cannot fully capture all behaviors under these assumptions due to the restrictions in our understanding and potential constraints of numerical methods.

Yes / An experimental study is presented here to understand the stress transmission characteristics under different geometrical arrangements of particulates inside a narrow chamber subjected to axial compression loading. The multi-grain systems considered here are face-centred, simple cubic and poly-dispersed structures, as well as inclusions embedded inside seeded, unseeded and cohesive powder bed of Durcal (calcium carbonate). The distribution of the maximum shear stress, direction of the major principal stress and shear stress concentration factor were obtained using photo stress analysis tomography (PSAT). The results show that the maximum shear stress distribution in the simple cubic structure is chain-like and self-repetitive, i.e., a single grain behaviour is representative of the whole system. This is not the case in the case of other granular packing. In the case of the inclusion surrounded by powder media, the maximum shear stress distribution in the inclusion occurs through ring-like structures, which are different from those observed in the structured granular packing. This tendency increases for an increase in the cohesivity of the surrounding particulates. In the granular systems, the direction of the major principal stress is mostly orthogonal to the direction of loading except in some particles in the random granular packing. In the case of inclusion surrounded by Durcal particulates, the directional of the major principal stress acts along the direction of the axial loading except in the ring region where this tends to be oblique to the direction of axial loading. Estimates of the shear stress concentration factor (k) show that, k tends to be independent of the structural arrangement of granular packing at higher load levels. In the case of inclusion surrounded by powder bed, k for the seeded granulated particulate bed is mostly independent of the external load levels. In the case of unseeded particulate (granulated) bed, a fluctuation in k is observed with the loading level. This suggests that the seeded granules could distribute stresses in a stable manner without much change in the nature of shear stress-transmitting fabric of the particulate contacts under external loading. An increase in the cohesion of particulate bed results in more plastic deformation as shown by the differential shear stress concentration factor. The results reported in this study show the usefulness of optical stress analysis to shed some scientific lights on unravelling some of the complexities of particulate systems under different structural arrangements of grains and surrounding conditions of the inclusions in particulate media.

Les surfaces et interfaces rugueuses sont rencontrées dans de nombreuses situations en mécanique et physique des solides. En particulier, une surface ou interface considérée comme lisse à une échelle donnée se révèle souvent rugueuse à autre échelle plus petite. Ce travail étudie les interfaces planes et courbées dont la rugosité peut être raisonnablement décrite comme des ondulations périodiques. Il a pour objectif de modéliser ces interfaces dans des composites et de déterminer leurs effets sur les propriétés effectives élastiques et conductrices des composites concernés. L'approche élaborée pour atteindre cet objectif consiste d'abord à utiliser l'analyse asymptotique pour modéliser une zone d'interface rugueuse comme une interphase hétérogène uniquement suivant son épaisseur et ensuite à faire appel à des schémas micromécaniques pour quantifier les influences de cette interphase sur les propriétés effectives. Ce travail considère trois types de composites dans lesquels de s interfaces périodiquement ondulées sont présentes : composites stratifiés, fibreux et à inclusions. Les résultats obtenus pour ces composites contribuent au développement de la micromécanique et apportent des solutions à des problèmes d'intérêt pratique rencontrés en physique et mécanique des matériaux hétérogènes / Rough surfaces and interfaces are encountered in many situations in mechanics and physics of solids. In particular, a surface or interface considered smooth at a given scale turns out often to be rough at another smaller scale. This work studies the flat and curved interfaces whose roughness can be reasonably described as periodic undulations. It aims to model these interfaces in composites and to determine their effects on the effective elastic and conductive properties of the composites in question. The approach elaborated to achieve this objective consists first in using asymptotic analysis to model a zone of rough interface as an interphase being heterogeneous only along its thickness direction and then in resorting to some micromechanical schemes to quantify the influences of the interphase on the effective properties. This work considers three types of composites in which periodically corrugated interfaces are present: laminated, fibrous and particulate composites. The results obtained for these composites contribute to the development of micromechanics and provide solutions to problems of practical interest encountered in physics and mechanics of heterogeneous materials

L'objectif de cette thèse de doctorat est de contribuer à une meilleure compréhension et modélisation de la rupture ductile lors de la mise en forme des métaux. Cette mise en forme se réalise en général par une série de chargements thermomécaniques où de multiples paramètres comme le type et la direction de chargement varient. Des outils de simulations prédictifs sont nécessaires pour modéliser les mécanismes de rupture, et ensuite optimiser les coûts de production.La rupture ductile des matériaux métalliques est précédée par la détérioration progressive de leur capacité de charge due à la germination, croissance, et coalescence de cavités microscopiques. Dans ce travail, une approche micromécanique est développée afin de conduire des simulations éléments finis réalistes et à champ complet de la rupture ductile à l'échelle microscopique. Des méthodes de génération et d'adaptation de maillage s'appuyant sur des fonctions de niveau sont proposées pour discrétiser la microstructure. Avec ces méthodes, les propriétés géométriques des fonctions de niveau sont conservées, ainsi que le volume et la morphologie de chaque composante de la microstructure, et ce pour de grandes déformations plastiques. Ces méthodes numériques sont étendues pour permettre la modélisation de fissures aux interfaces entre certaines composantes de la microstructure, ou à l'intérieur même de ces composantes. Une nouvelle méthode de détection de contact par adaptation de maillage est aussi développée.L'intérêt de ces développements numériques et modèles micromécaniques est démontré tout d'abord pour des microstructures générées statistiquement. Ensuite, une nouvelle méthodologie est proposée pour modéliser des microstructures réelles (laminographie in-situ) avec des conditions aux limites mesurées expérimentalement (corrélation d'images volumiques). / The present PhD thesis aims at a better understanding and modeling of ductile fracture during the forming of metallic materials. These materials are typically formed using series of thermomechanical loads where many parameters such as loading type and direction vary. Predictive numerical tools are necessary to model fracture mechanisms, and then optimize production costs.Ductile fracture in metallic materials is the result of a progressive deterioration of their load carrying capacity due to the nucleation, growth, and coalescence of microscopic voids. In this work, a micromechanical approach is developed in order to conduct realistic full field finite element simulations of ductile fracture at the microscale. Meshing and remeshing methods relying on the use of Level-Set functions are proposed to discretize the microstructure. Thanks to these methods, the geometric properties of Level-Set functions are preserved, as well as the volume and morphology of each component of the microstructure, even at large plastic strains. These numerical methods are extended to account for cracks and model the failure of some components of the microstructure, or interfaces between them. A new contact detection method based on mesh adaptation is also developed.The interest of these numerical developments and micromechanical models is first demonstrated at the scale of representative volume elements with statistically generated microstructures. Then, a new methodology is proposed to conduct simulations of real microstructures observed via in-situ X-ray laminography, with boundary conditions that are measured using digital volume correlation techniques.