Dissertations / Theses on the topic 'Mechanical Representative Elementary Volume'

The equivalent continuum approach uses equivalent propertiesof rock mass as the input data for a continuum analysis. Thisis a common modeling method used in the field of rock mechanicsand hydrogeology. However, there are still unresolvedquestions; how can the equivalent properties be determined andis the equivalent continuum approach suitable for modeling thediscontinuous fractured rock mass.

The purpose of this paper is to establish a methodology todetermine the equivalent hydraulic and mechanical properties offractured rock masses by explicit representations of stochasticfracture systems, to investigate the scale-dependency of theproperties, and to investigate the conditions for theapplication of the equivalent continuum approach for thefractured rock masses. Geological data used for this study arefrom the site characterization of Sellafield, Cumbria, UK. Aprogram for the generation of stochastic Discrete FractureNetwork (DFN) is developed for the realization of fractureinformation and ten parent DFN models are constructed based onthe location, trace length, orientation and density offractures. Square models with the sizes varying from 0.25 m× 0.25 m to 10 m × 10 m are cut from the center ofthe each parent network to be used for the scale dependencyinvestigation. A series of the models in a parent network arerotated in 30 degrees interval to be used for investigation oftensor characteristic. The twodimensional distinct elementprogram, UDEC, was used to calculate the equivalentpermeability and compliance tensors based on generalizedDarcy’s law and general theory of anisotropic elasticity.Two criteria for the applicability of equivalent continuumapproach were established from the investigation: i) theexistence of properly defined REV (Representative ElementaryVolume) and ii) existence of the tensor in describing theconstitutive equation of fractured rock The equivalentcontinuum assumption cannot be accepted if any one of the abovetwo criteria is not met. Coefficient of variation and meanprediction error is suggested for the measures toquantitatively evaluate the errors involved in scale dependencyand tensor characteristic evaluation.

Equivalent permeability and mechanical properties (includingelastic modulus and Poisson’s ratios) determined onrealistic fracture network show that the presence of fracturehas a significant effect on the equivalent properties. Theresults of permeability, elastic moduli and Poisson's ratioshow that they narrow down with the increase of scale andmaintain constant range after a certain scales with someacceptable variation. Furthermore, Investigations of thepermeability tensor and compliance tensor in the rotated modelshow that their tensor characteristics are satisfied at acertain scale; this would indicate that the uses of theequivalent continuum approach is justified for the siteconsidered in this study.

The unique feature of the thesis is that it gives asystematic treatment of the homogenization and upscaling issuesfor the hydraulic and mechanical properties of fractured rockswith a unified approach. These developments established a firmfoundation for future application to large-scale performanceassessment of underground nuclear waste repository byequivalent continuum analysis.

Keywords :Equivalent continuum approach, Equivalentproperty, Representative Elementary Volume (REV), DistinctElement Method, Discrete Fracture Network (DFN)

Cette thèse vise à approfondir la compréhension des relations entre le module d’élasticité d’un polypropylène isotactique (iPP) et sa microstructure à différentes échelles. Une approche expérimentale multi-échelle originale est développée, combinant essais d’indentation et microscopie à force atomique (AFM) pour la caractérisation du module d’élasticité et de la morphologie tridimensionnelle des sphérolites. Le travail s'articule autour de quatre axes : (i) la caractérisation de la morphologie sphérolitique par AFM, (ii) des essais d’indentation à diverses échelles en utilisant différentes techniques (AFM en mode mécanique, nanoindentation, et macro-indentation), (iii) la caractérisation du module d’élasticité au sein des sphérolite à travers des cartographies de module obtenue par nanoindentation et par AFM en mode mécanique, et (iv) l’évaluation d’un volume élémentaire représentatif (VER) mécanique à partir d’essais d’indentation sphérique.Un protocole original a permis de produire des échantillons massifs de iPP avec une surface plane, peu rugueuse et sans attaque chimique, conservant ainsi la microstructure tridimensionnelle de surface. Les résultats révèlent des éléments nouveaux sur la microstructure des sphérolites et la nanostructure lamellaire de la phase α. Outre les observations classiques (formes en gerbe ou rosette), une échelle intermédiaire est identifiée : les branches radiales des sphérolites, de taille micrométrique, constituées de lamelles cristallines orientées orthoradialement. Ces lamelles adoptent une organisation « lath-like » dans les branches et « cross-hatching » dans les zones de fermeture. La longue période (Lp) moyenne est mesurée localement par AFM, et est cohérente avec la littérature (SAXS).Les cartographies par nanoindentation ont montré un gradient décroissant du module du centre vers les bords des sphérolites. Les branches situées sur les axes principaux de croissance affichent les modules les plus élevés, tandis que les zones latérales montrent des valeurs plus faibles. Cette variation est attribuée à la densité, à l'organisation ou à l’orientation des lamelles. À l’échelle lamellaire, les cartographies obtenues par AFM en mode mécanique montrent des hétérogénéités significatives. Certaines branches affichent des modules élevés, probablement liés à la microstructure sous la surface. Une transition est observée, avec des valeurs plus faibles au centre et plus élevées en périphérie, marquant un changement de module avec la croissance radiale. Toutefois, aucune corrélation directe n'a été établie avec des paramètres géométriques comme la longue période Lp ou l'angle d’émergence des lamelles, suggérant que ces paramètres microstructuraux ne suffisent pas à eux seuls à capturer la complexité de la microstructure. Une étude d’indentation sphérique multi-échelle a permis d’explorer les effets d’échelle sur le module d’élasticité du iPP. Les résultats révèlent que les modules mesurés par AFM sont significativement plus élevés que ceux obtenus par nanoindentation et macro-indentation, ces dernières présentant des valeurs assez similaires. Plusieurs hypothèses sont proposées et discutées pour expliquer cette différence, notamment le volume sondé, la vitesse de sollicitation et le cadre d'analyse. L’échelle de transition vers un VER mécanique n’est pas précisément déterminée, mais les résultats suggèrent qu’elle se situe à l’échelle intra-sphérolitique, lorsque plusieurs branches sont sondées. Cette évaluation pourrait varier avec d'autres microstructures. Enfin, l’étude des transitions entre techniques d’indentation a montré que varier la taille des pointes offre un gain limité sur le volume sondé, révélant ainsi les limites des équipements actuels pour explorer pleinement ces transitions d’échelle
The aim of this thesis is to gain a deeper understanding of the relationships between the elastic modulus of isotactic polypropylene (iPP) and its microstructure at different scales. An original multi-scale experimental approach is developed, combining indentation tests and atomic force microscopy (AFM) to characterize the elastic modulus and three-dimensional morphology of spherulites. The work is structured around four axes: (i) characterization of spherulitic morphology by AFM, (ii) indentation tests at various scales using different techniques (AFM in mechanical mode, nanoindentation, and macro-indentation), (iii) characterization of elastic modulus within spherulites through modulus mappings obtained by nanoindentation and AFM in mechanical mode, and (iv) evaluation of a mechanical representative elementary volume (REV) from spherical indentation tests. An original protocol was used to produce bulk iPP samples with a flat, slightly rough surface and without chemical etching, thus preserving the three-dimensional surface microstructure. The results reveal new insights into the microstructure of spherulites and the lamellar nanostructure of the α-phase. In addition to the classic observations (sheaf or rosette shapes), an intermediate scale is identified: the micrometer-sized radial branches of spherulites, made up of orthoradially oriented crystalline lamellae. These lamellae adopt a “lath-like” organization in the branches and “cross-hatching” in the closure zones. The average long period (Lp) is measured locally and is consistent with the literature (SAXS).Nanoindentation mapping showed a decreasing modulus gradient from the center to the edges of the spherulites. Branches located on the main growth axes show the highest moduli, while lateral areas show lower values. This variation is attributed to the density, organization or orientation of the lamellae. At lamellar scale, AFM in mechanical mode mappings show significant heterogeneity. Some branches display high moduli, probably linked to the subsurface microstructure. A transition is observed, with lower values in the center and higher at the periphery, marking a change in modulus with radial growth. However, no direct correlation was established with geometric parameters such as the long period Lp or the lamella emergence angle, suggesting that these microstructural parameters alone are not sufficient to capture the complexity of the microstructure. A multi-scale spherical indentation study explored the effects of scale transition on the elastic modulus of iPP. The results reveal that the moduli measured by AFM are significantly higher than those obtained by nano-indentation and macro-indentation, the latter presenting fairly similar values. Several hypotheses were proposed and discussed to explain this difference, including the volume probed, the strain rate and the analysis framework. The scale transition to a mechanical REV is not precisely determined, but the results suggest that it lies at the intra-spherulitic scale, when several branches are probed. This assessment could vary with other microstructures. Finally, the scale transition study between indentation techniques showed that varying tip size offers limited gain in probed volume, revealing the limitations of current equipment to fully explore these scale transitions

In this thesis, the effects of size and stress on permeability, deformability and strength of fractured rock masses are investigated. A comparison study was carried out to examine the effects of considering, or not considering, the correlation between distributions of fracture apertures and fracture trace lengths on the hydro-mechanical behavior of fractured rocks. The basic concepts used are the fundamental principles of the general theory of elasticity, Representative Elementary Volume (REV), the tensor of equivalent permeability, and the strength criteria of the fractured rocks. Due to the size and stress dependence of the hydro-mechanical properties of rock fractures, the overall effective (or equivalent) hydro-mechanical properties of the fractured rocks are also size and stress-dependent. However, such dependence cannot be readily investigated in laboratory using small samples, and so numerical modeling becomes a necessary tool for estimating their impacts. In this study, a closed-form relation is established for representing the correlation between a truncated lognormal distribution of fracture apertures and a truncated power law distribution of trace lengths, as obtained from field mapping. Furthermore, a new nonlinear algorithm is developed for predicting the relationship between normal stress and normal displacement of fractures, based on the Bandis model and the correlation between aperture and length. A large number of stochastic Discrete Fracture Network (DFN) models of varying sizes were extracted from some generated large-sized parent realizations based on a realistic fracture system description from a site investigation programme at Sellafield, UK, for calculating the REV of hydro-mechanical properties of fractured rocks. Rotated DFN models were also generated and used for evaluation of the distributions of directional permeabilities, such that tensors of equivalent permeability could be established based on stochastically established REVs. The stress-dependence of the permeability and the stress-displacement behaviour were then investigated using models of REV sizes. The Discrete Element Method (DEM) was used for numerical simulation of the fluid flow, deformability properties and mechanical strength behavior of fractured rocks. The results show significant scale-dependency of rock permeability, deformability and strength, and its variation when the correlation between aperture and trace length of fractures are concerned, with the overall permeability and deformability more controlled by dominating fractures with larger apertures and higher transmissivity and deformability, compared with fracture network models having uniform aperture. As the second moment of aperture distribution increases, a fractured rock mass shows more discrete behavior and an REV is established in smaller value of second moment with much larger model size, compared with the models with uniform fracture aperture. When the fracture aperture pattern is more scattered, the overall permeability, Young’s modulus and mechanical strength change significantly. The effect of stress on permeability and fluid flow patterns in fractured rock is significant and can lead to the existence or non-existence of a permeability tensor. Stress changes the fluid flow patterns and can cause significant channeling and the permeability tensor, and REV may be destroyed or re-established at different applied stress conditions. With an increase in the confining stress on the DEM models, the strength is increased. Compared with the Hoek-Brown criterion, the Mohr-Coulomb strength envelope provides a better fit to the results of numerical biaxial compression tests, with significant changes of the strength characteristic parameters occurring when the second moment of the aperture distribution is increased.
QC 20100702

This thesis presents a systematic numerical modeling framework to simulate the stress-deformation and coupled stress-deformation-flow processes by performing uniaxial and biaxial compressive tests on fractured rock models with considering the effects of different loading conditions, different loading directions (anisotropy), and coupled hydro-mechanical processes for evaluating strength and deformability behavior of fractured rocks. By using code UDEC of discrete element method (DEM), a series of numerical experiments were conducted on discrete fracture network models (DFN) at an established representative elementary volume (REV), based on realistic geometrical and mechanical data of fracture systems from field mapping at Sellafield, UK. The results were used to estimate the equivalent Young’s modulus and Poisson’s ratio and to fit the Mohr-Coulomb and Hoek-Brown failure criteria, represented by equivalent material properties defining these two criteria. The results demonstrate that strength and deformation parameters of fractured rocks are dependent on confining pressures, loading directions, water pressure, and mechanical and hydraulic boundary conditions. Fractured rocks behave nonlinearly, represented by their elasto-plastic behavior with a strain hardening trend. Fluid flow analysis in fractured rocks under hydro-mechanical loading conditions show an important impact of water pressure on the strength and deformability parameters of fractured rocks, due to the effective stress phenomenon, but the values of stress and strength reduction may or may not equal to the magnitude of water pressure, due to the influence of fracture system complexity. Stochastic analysis indicates that the strength and deformation properties of fractured rocks have ranges of values instead of fixed values, hence such analyses should be considered especially in cases where there is significant scatter in the rock and fracture parameters. These scientific achievements can improve our understanding of fractured rocks’ hydro-mechanical behavior and are useful for the design of large-scale in-situ experiments with large volumes of fractured rocks, considering coupled stress-deformation-flow processes in engineering practice.

QC 20141111

Thesis (Nav. E. and S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 67-69).
The importance of Lithium-ion batteries continues to grow with the introduction of more electronic devices, electric cars, and energy storage. Yet the optimization approach taken by the manufacturers and system designers is one of test and build, an approach that nearly every other industry has long abandoned. A computational model is required to reduce the expensive build-test cycle and allow safer, cheaper batteries to be built. The path to building this computational model will involve many different processes and one of those processes dictates the homogenizing of the interior of the battery casing by treating the interior as a homogenized Representative Volume Element. This study explains this process and outlines a procedure for the development of this particular model for both cylindrical and prismatic / pouch cells. Over twenty different mechanical tests were performed on fully-discharged cylindrical and pouched / prismatic lithium-ion batteries, in casings and without casings under multiple loading conditions. These included lateral indentation by a rod, axial compression, through-thickness compression, in-plane unconfined compression, in-plane confined compression, hemispherical punch indentation and three-point bending. Extensive testing on the battery cell and jelly roll of 18650 lithium ion cylindrical cell, combined with the use of analytical solutions to estimate material properties of the cell, yielded the development of a finite element model. It was found that the suitably calibrated model of high density compressible foam provided a very good prediction of the crash behavior of cylindrical battery cell subjected to high intensity lateral and axial loads. For the prismatic / pouch cell, the measured load-displacement data allowed calculation of the individual compression stress-strain curves for the separator, the active anode and cathode materials. The average stress-volumetric strain relation was derived from averaging the properties of individual layers as well as from direct measurement on the bare cell. This information was then used as an input to the FE model of the cell. The model was composed of shell elements representing the Al and Cu foil and solid elements for the active material with a binder lumped together with the separator. Very good correlation was obtained between LS-Dyna numerical simulation and test results for the through-thickness compression, punch indentation and confined compression. Closed form solutions were also derived for the latter three problems which helped explain the underlying physics and identified important groups of parameters. It was also demonstrated that a thin Mylar pouch enclosure provided considerable reinforcement and in some cases changed the deformation and failure mechanism. This paper reports on the results generated for the Li-ion Battery Consortium at MIT.
by Richard Lee Hill, Sr.
Nav.E.and S.M.

O estudo numérico do comportamento estrutural de materiais compostos apresenta-se, desde os últimos anos, como um campo muito fértil de pesquisas, o que justifica o crescimento exponencial de trabalhos científicos nesta área. Atualmente é possível desenhar as propriedades físicas do material adequando-os ao uso que se queira dar a eles. Especificamente quanto às propriedades mecânicas vinculadas a função estrutural que o material em estudo possa ter, estas podem, na atualidade, ser quantificadas, modificadas e otimizadas. No presente trabalho, explora-se um material composto formado por uma matriz polimérica e uma segunda fase particulada com distribuição aleatória. Para realizar esse estudo foi utilizado o método dos elementos discretos e o método dos elementos finitos. No primeiro caso é apresentado um estudo onde se realizam tentativas de determinar o elemento de volume representativo considerando o comportamento do material como não-linear. No segundo caso, aplicando o método dos elementos finitos, realiza-se um estudo considerando a matriz e a fase particulada com comportamento elástico linear, determinando o elemento de volume representativo e comparando os resultados, em termos de constantes elásticas homogeneizadas, com propostas teóricas fornecidas pela micromecânica clássica. Um estudo da convergência da malha e exercícios de otimização foram realizados sobre o composto simulado. Finalmente, realiza-se um estudo não-linear através do método dos elementos finitos, onde a matriz é elástica e a fase particulada hiperelástica, onde se determina o elemento de volume representativo e se faz aplicações para verificação da eficácia dos resultados.
The numerical study of the composite material mechanical behavior has shown lately a fertile field of research, which justifies the exponential growing of scientific works in this area. Nowadays it is possible to design the material properties adapting them to the usage that we want to give them. Specifically, regarding to the mechanical properties, there are methods that allow us to modify them in a rational way to reach different objectives. In the present work, different aspects are analyzed of a composite material built with a polymeric matrix and a second particulate phase with random distribution. The Discrete Element Method (DEM) and the Finite Element Method (FEM) were used to carry out the present work. Firstly, an application of DEM, a study of different alternatives is shown to determine the volume representative element (RVE) considering the non-linear behavior of the studied material. Secondly, an application of FEM, a study considering the matrix and particulate phase, both, with linear elastic behavior. This application consists on computing the RVE and comparing these results with analytical proposals available in the Micromechanics classical bibliography. A mesh convergence study of the FEM models used and simple applications of optimization are also presented. Finally, another application of FEM is presented. In this case a non linear study is shown, where the matrix is considered linear elastic, and the particulate phase is hyperelastic. In this case the RVE was determined and some applications to verify the consistency of the results obtained are presented.

碩士
國立中央大學
土木工程學系
105
This study presents the representative elementary volume (REV) of P32 (fracture intensity) and hydraulic conductivity of fractured rock mass. Discrete fracture network (DFN) generated by FracMan is adopted to create rock mass models. A series of parametric studies including dip angle, dip direction, Fisher constant κ, size of rock mass model, shape of rock mass model, specimen volume, fracture diameter, and P32 were investigated to study the REV of P32. Based on the results of the parametric studies, a novel equation to quantify the COV (Coefficient of variance) of P32 in terms of specimen volume, fracture diameter and P32 was established. A precise REV size can be obtained easily by assigning the acceptable COV. Thereafter, some case studies were used to verify the proposed novel equation. Conventional Oda and Oda gold were adopted to estimate the hydraulic conductivity of the fractured rock mass. By using Oda conventional, a series of parametric studies including specimen volume, fracture diameter, P32, transmissivity, and aperture were investigated to study the REV of hydraulic conductivity. Subsequently, that REV of hydraulic conductivity was compared with the REV of P32. In the other hand, by using Oda gold, only P32 was chosen as parametric study. Eventually, a proposed new method was conducted by examining the Monte Carlo simulation for REV of hydraulic conductivity determination.

碩士
國立中正大學
機械工程所
96
High strength and weight reduction are the primary material qualification in automobile industry and aviation technology as well. Because of the fabrication of the composites selected Mg and Mg alloy as the matrix to improve the elastic modulus, yielding strength, and tensile strength, so the simulation of the Mg-Al2O3p composites had been investigated to observed the elastic modulus. The single Representative Volume Element (RVE) cube model was used to simulate the unit cell structure of the composite with both conditions of numerical homogenization Technique and Periodic boundary condition to get the mechanical properties of the composite in macro and complex scales. From the results of the analysis in RVE model, the distribution graphs of the stress, strain and displacement on the surface of the RVE are plotted. It shows that the elastic modulus increased with increasing of the volume percentage.

碩士
國立臺北科技大學
資源工程研究所
105
In recent years, the large-scale construction projects and environmental resources related issues had brought attentions and rapid development on hydrogeology and other academic field connected to it. Rock engineering, including large-scale underground laboratory, tunnel excavation and hydrogeological well site, requires a certain degree of understanding on hydrogeology and hydraulic parameters, in order to facilitate subsequent planning and related construction. However, the presence of discontinuities in rock mass generates heterogeneity and anisotropy in its engineering characteristics, increasing variation of hydraulic and conductivity parameters, resulting in difficulty for determining representative parameters. Investigation and characterization of hydrogeological parameters of fracture rock masses are crucial to underground water exploiting. Among which, defining the hydrogeological representative elementary volume of the site is one of the key items. How to evaluate the hydrogeological unit to the scale of the target rock engineering is an important issue in hydrogeological parameters characterization. Based on previous research results, this thesis present an assessment process for representative elementary volume on hydraulic parameter characterization on account of a hydraulic parameter characterization model for fractured rock mass. Investigation and statistical test are applied to estimate the variation degrees of representative elementary volume in site and associated hydraulic conductivity in rock mass, which further determine the scale influence on each hydraulic characteristic parameters, the methodology of the establishment and extension of application is through by Heshe hydrogeological well site, and another tunnel case project in initiative in north Taiwan. The evaluation method of representative elementary volume in hydraulic characteristic establish by statistical error propagation theory to calculate the varying degrees between the characteristic parameters and hydraulic conductivity, and the empirical formula of different hydraulic conductivity is discussed to find the variation range and plotted out different scales in a result. In order to understand the behavior of hydraulic conductivity associated with representative elementary volume changes, this research applies groundwater modeling system to establish numerical model and analysis it. Firstly, the anisotropy is simulated with a single element, the error between the two elements is calculated by numerical solution and analytic solution. Then, convert the goal of simulation scale to in-situ cross-hole pumping test which in heshe well site. Secondly, parameter sensitivity analysis is carried out to understand the representative elementary volume and its related parameters. Scale variation is using for complete numerical simulation methodology parallel verification, and establish the accuracy and correctness of the model. The case study is aimed at extending the application of different representative elementary volumes on the volume of seepage flow caused by tunnel excavation, which extend the application of methodologies in a large number of site surveys and numerical models. The results show that the representative elementary volume evaluation program can effectively describe the change of the hydraulic characteristic parameters and the hydraulic conductivity coefficient with the scale variation by the statistical error propagation accumulation theory, and verify the groundwater anisotropy by numerical simulation. The related parameter sensitivity analysis shows that the numerical solution and the analytical solution will produce a certain range of errors in the setting of the boundary condition. The determination of the error value can provide the numerical model to improve the accuracy and correctness of the subsequent research. The hydraulic characteristic parameters of representative elementary volumes are on different scales, which changed in the groundwater seepage caused by tunneling, that with a certain degree of influence of groundwater through the three-dimensional simulation. We provide a valuable technical reference from the conceptual model, narrative model, and hydraulics model all the way to numerical model, through the outcome of methodology in designing verification and applying in this study.

Aluminum alloys have broad applications in aerospace, automotive, and defense industries as structural material due to the low density, high-specific strength, good castability and formability. However, aluminum alloys commonly suffer from problems such as low yield strength, low stiffness, and poor wear and tear resistance, and therefore are restricted to certain advanced industrial applications. To overcome the problems, one promising method is the fabrication of aluminum matrix composites (AMCs) by introducing ceramic reinforcements (fibers, whiskers or particles) in the metal matrix. AMCs typically possess advanced properties than the matrix alloys such as high specific modulus, strength, wear resistance, thermal stability, while remain the low density. Among the AMCs, particulate reinforced aluminum matrix composites (PRAMCs) are advantageous for their isotropic properties, ease of fabrication, and low costs. Particularly, the PRAMCs with in-situ particulate reinforcements have received great interest recent years. The in-situ fabricated particles are synthesized in an aluminum matrix via chemical reactions. They are more stable and finer in size, and have a more uniform distribution in the aluminum matrix and stronger interface bonding with aluminum matrix, compared to the ex-situ particulate reinforcements. As a consequence, the in-situ PRAMCs have superior strength and mechanical properties as advanced engineering materials for a broad range of industrial applications.

This dissertation focuses on the investigation of high strength aluminum matrix composites reinforced with in-situ particulates. The first chapter provides a brief introduction for the studied materials in the dissertation, including the background, the scope, the significance and the research questions of the study. The second chapter presents the literature review on the basic knowledge, the fabrication methods, the mechanical properties of in-situ PRAMCs. The strengthening mechanisms and strategies of in-situ PRAMCs are summarized. Besides, the micromechanical simulation is introduced as a complementary methodology for the investigation of the microstructure-properties relationship of the in-situ PRAMCs. The third chapter shows the framework and methodology of this dissertation, including material preparation and material characterization methods, phase diagram method and finite element modelling.

In Chapter 4, the microstructures and mechanical properties of in-situ Al₃Ti particulate reinforced A356 composites are investigated. The microstructure and mechanical properties of in-situ 5 vol. % Al₃Ti/A356 composites are studied either taking account of the effects of T6 heat treatment and strontium (Sr) addition or not. Chapter 5 studies the evolution of intermetallic phases in the Al-Si-Ti alloy during solution treatment, based on the work of Chapter 4. The as-cast Al-Si-Ti alloy is solution treated at 540 °C for different periods between 0 to 72 h to understand the evolution of intermetallic phases. In Chapter 6, a three-dimensional (3D) micromechanical simulation is conducted to study the effects of particle size, fraction and distribution on the mechanical behavior of the in-situ Al₃Ti/A356 composite. The mechanical behavior of the in-situ Al₃Ti/A356 composite is studied by three-dimensional (3D) micromechanical simulation with microstructure-based Representative Volume Element (RVE) models. The effects of hot rolling and heat treatment on the microstructure and mechanical properties of an in-situ TiB₂/Al2618 composite with minor Sc addition are investigated in Chapter 7. TiB₂/Al2618 composites ingots were fabricated in-situ via salt-melt reactions and subjected to hot rolling. The microstructure and mechanical properties of the TiB₂/Al2618 composite are investigated by considering the effects of particle volume fraction, hot rolling thickness reduction, and heat treatment.

Composite materials show heterogeneity at different length scales. hence concurrent multiscale analysis is the only reliable method to analyze them. But unfortunately there is no concurrent multi-scale strategy that is efficient, and accurate while addressing all kinds of problems. This lack of reliability is partly because there is no micro-mechanical model which inherently keeps all relevent global information with it. This thesis tries to fill this gap. The presented micro-mechanical model not only homogenizes the micro-structure but also keeps the global information with it. Most of the micro-mechanical models in the literature extract the Representative Volume Element (RVE) from the continuum for analysis which results in loss of information and accuracy. In the present approach also, the RVE has been extracted from the continuum but with the major difference that all the macro/meso-scopic parameters are accounted for. Five macro/meso-scopic one dimensional parameters have been defined which completely define the effect of continuum. 11 for one dimensional stretch, _1 for torsion, __ (_ = 2, 3) for bending and _33 for uniform pressurization due to the presence of the continuum. Further, the above macro/meso-scopic parameters are proven, by the asymptotic, theory to be constant at a cross section but vary, in general, over the length of the fiber. Hence, the analysis is valid for any location and is not restricted to any local domain. Three major problems have been addressed: • Homogenization and analysis of RVE without any defects • Homogenization and analysis of RVE with fiber-matrix de-bonding • Homogenization and analysis of RVE with radial matrix cracking. Variational Asymptotic Method (VAM) has been used to solve the above mentioned problems analytically. The results have been compared against standard results in the literature and against 3D FEA. At the end, results for “Radial deformation due to torsion” problem will be presented which was solved “accidentally.”

Composite materials show heterogeneity at different length scales. hence concurrent multiscale analysis is the only reliable method to analyze them. But unfortunately there is no concurrent multi-scale strategy that is efficient, and accurate while addressing all kinds of problems. This lack of reliability is partly because there is no micro-mechanical model which inherently keeps all relevent global information with it. This thesis tries to fill this gap. The presented micro-mechanical model not only homogenizes the micro-structure but also keeps the global information with it. Most of the micro-mechanical models in the literature extract the Representative Volume Element (RVE) from the continuum for analysis which results in loss of information and accuracy. In the present approach also, the RVE has been extracted from the continuum but with the major difference that all the macro/meso-scopic parameters are accounted for. Five macro/meso-scopic one dimensional parameters have been defined which completely define the effect of continuum. 11 for one dimensional stretch, _1 for torsion, __ (_ = 2, 3) for bending and _33 for uniform pressurization due to the presence of the continuum. Further, the above macro/meso-scopic parameters are proven, by the asymptotic, theory to be constant at a cross section but vary, in general, over the length of the fiber. Hence, the analysis is valid for any location and is not restricted to any local domain. Three major problems have been addressed: • Homogenization and analysis of RVE without any defects • Homogenization and analysis of RVE with fiber-matrix de-bonding • Homogenization and analysis of RVE with radial matrix cracking. Variational Asymptotic Method (VAM) has been used to solve the above mentioned problems analytically. The results have been compared against standard results in the literature and against 3D FEA. At the end, results for “Radial deformation due to torsion” problem will be presented which was solved “accidentally.”

Mechanics of structure genome (MSG) is a unified homogenization theory that provides constitutive modeling of three-dimensional (3D) continua, beams and plates. In present work, the author extends the MSG to study the buckling of structures such as stiffened and sandwich panels. Such structures are usually slender or flat and easily buckle under compressive loads or bending moments which may result in catastrophic failure.