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Il est bien établi que les propriétés mécaniques et rhéologiques d'une large classe de matériaux vitreux amorphes met en jeu - contrairement aux dislocations dans les cristaux - des rearrangements structuraux localisés formant par un processus de cascade des bandes de cisaillements. Cette localisation de la déformation est observée dans divers systèmes vitreux ainsi que dans des simulations numériques. Cette réponse mécanique complexe reste mal comprise à une échelle microscopique et il n'est pas clair si l'écoulement plastique peut être associé à une origine structurale locale ou à des processus purement dynamiques.Dans cette thèse nous envisageons ces problématiques à l'aide de simulations atomiques athermales sur un système Lennard-Jones modèle. Nous calculons le tenseur élastique moyenné localement sur une échelle nanométrique. A cette échelle, le verre est assimilable à un matériau composite comprenant un échafaudage rigide et des zones fragiles. L'étude détaillée de la déformation plastique à différents taux de cisaillement met en évidence divers régimes d'écoulement. En dessous d'un taux de cisaillement critique dépendant de la taille du système, la réponse mécanique atteind une limite quasistatique (effets de taille fini, cascades d'événements plastiques, contrainte seuil) alors que pour des taux de cisaillement plus importants les propriétés rhéologiques sont fixées par le taux de cisaillement imposé. Dans ce régime nous mettons en évidence la croissance d'une longueur de coopérativité dynamique et discutons de sa dépendance avec le taux de cisaillements.

In composite materials, transverse shear modulus is a critical moduli parameter for designing complex composite structures. For dependable mathematical modeling of mechanical behavior of composite materials, an accurate estimate of the moduli parameters is critically important as opposed to estimates of strength parameters where underestimation may lead to a non-optimal design but still would give one a safe one. Although there are mechanical and empirical models available to find transverse shear modulus, they are based on many assumptions. In this work, the model is based on a three-dimensional elastic finite element analysis with multiple cells. To find the shear modulus, appropriate boundary conditions are applied to a three-dimensional representative volume element (RVE). To improve the accuracy of the model, multiple cells of the RVE are used and the value of the transverse shear modulus is calculated by an extrapolation technique that represents a large number of cells. Comparing the available analytical and empirical models to the finite element model from this work shows that for polymeric matrix composites, the estimate of the transverse shear modulus by Halpin-Tsai model had high credibility for lower fiber volume fractions; the Mori-Tanaka model was most accurate for the mid-range fiber volume fractions; and the Elasticity Approach model was most accurate for high fiber volume fractions. Since real-life composites have voids, this study investigated the effect of void fraction on the transverse shear modulus through design of experiment (DOE) statistical analysis. Fiber volume fraction and fiber-to-matrix Young’s moduli ratio were the other influencing parameters used. The results indicate that the fiber volume fraction is the most dominating of the three variables, making up to 96% contribution to the transverse shear modulus. The void content and fiber-to-matrix Young’s moduli ratio have negligible effects. To find how voids themselves influence the shear modulus, the transverse shear modulus was normalized with the corresponding shear modulus with a perfect composite with no voids. As expected, the void content has the largest contribution to the normalized shear modulus of 80%. The fiber volume fraction contributed 12%, and the fiber-to-matrix Young’s moduli ratio contribution was again low. Based on the results of this work, the influences and sensitivities of void content have helped in the development of accurate models for transverse shear modulus, and let us confidently study the influence of fiber-to-matrix Young’s moduli ratio, fiber volume fraction and void content on its value.

Finite element analysis was implemented to evaluate the transverse shear modulus of a unidirectional glass/epoxy fiber-matrix composite based on pure shear displacement boundary conditions. Unit cells consisting of three-dimensional glass cylinders surrounded in square-cuboid epoxy matrices were modeled to represent "Representative Volume Element" (RVE) configurations in periodic and random-periodic square cell arrangements of variable size. Three RVEs were constructed and analyzed: A single unit cell, a 9-cell (3 x 3) array, and a 25-cell (5 x 5) array. Additionally, the unit cell was modeled to include an interphase. Three sets of cell arrangements were constructed and evaluated: a periodic square array, a transversely distributed random-periodic array, and a variable angularly aligned random-periodic array. Furthermore, scale and free-edge effects of the composites were studied by evaluating the shear modulus in incrementally increasing domains, as well as by isolating finite-sized domains called windows within the multiple-cell model, whereby the window is smaller than the array. Finite element software was subsequently utilized to create a three-dimensional mesh of the composite models studied. Each simulation consisted of exposing the respective domain to pure shear boundary conditions, whereby the model was subject to uniform transverse displacement along its boundary. Subsequent volumetric averaging resulted in computation of the apparent transverse shear modulus. The resulting numerically attained elastic shear modulus was then evaluated and compared to known predictive models in literature. It was shown that that the transverse random arrangement as well the random angular alignment of fibers within the composite structure had a marginal influence on the shear modulus. For random transverse distributions, a deviation in modulus of +1.5% was observed for the 25-cell array as compared to a periodic array of equal size. Similarly, a deviation of +0.3% was predicted for 25-cell arrays subject to random angular fiber misalignments up to ±0.143°, as compared 25-cell periodic arrays. Furthermore, increasing the composite medium by systematic, incremental augmentation model domains was shown to significantly lower the shear modulus in a convergent manner as G23 values dropped 33.5% from the nonhomogeneous single cell to the 9-cell model, and 2.6% from the same 9-cell to the 25-cell model, while observing the effects of a mesoscale window displayed little variance in modulus value as compared to the larger RVE from which the window was isolated from. Lastly, the predictive potential of the model developed by Sutcu for composites with interphases, and other commonly employed models for predicting the transverse shear modulus of unidirectional composites was also evaluated. Numerical results of nonhomogeneous interphase models for both periodic and random-periodic 25-cell arrays were found to be in excellent agreement with Sutcu's approximation. The shear modulus of the 25-cell, nonhomogeneous interphase model was found to lie within 3.5% of Sutcu's prediction. Volume averages for periodic arrays with no interphase were observed to lie in close proximity to Halpin-Tsai's model, displaying a variation of 7% for a 25-cell, single fiber model.

Ce travail de thèse combine des approches expérimentales et théoriques visant à caractériser l'impact des effets géomécaniques lors de l'injection de CO2 dans une formation de calcaire. La première partie est consacrée à l'étude expérimentale des évolutions des propriétés pétrophysiques et géomécaniques du calcaire étudié sous l'effet de l'altération chimique. L'évolution de la microstructure de la roche est également étudiée dans le but de comprendre les phénomènes observés à l'échelle macroscopique. La deuxième partie vise à définir, par approche micromécanique, un modèle de comportement géomécanique prenant en compte la dégradation des propriétés mécaniques de la roche carbonatée sous l'effet de l'attaque acide. L'élasticité et la résistance de la roche ont été modélisées et validées par les données expérimentales / This work composed of both experimental and theoretical studies aims at the characterization of carbonate rocks geomechanical evolution during CO2 injection. The first part of the study deals with the experimental work in order to characterize the petrophysical and geomechanical evolution of carbonate rock under chemical effect. Microstructure evolution has been investigated, in order to provider a better understanding of the observed phenomena at the macroscopic scale. The aim of the second part is to derive macroscopic properties of carbonate rock in framework of a micromechanical approach. The elastic moduli and effective strength in both intact and altered states have been computed and are compared with experimental data

Omnipresence of heterogeneity is conspicuous in all creations of nature. Heterogeneity manifests itself in many forms at different scales, both in time and space. Engineering domain being an exotic fusion of human creativity and ever-increasing demands exemplifies the ubiquity of heterogeneity. Surprisingly, the plethora of materials we see around seem to stem from myriad combination of few base materials identified as elements in chemistry. Further, a simple rearrangement of atoms in these materials leads to allotropes with startling contrasts in properties. Similarly, micro- and meso-scales in heterogeneous materials also dis-play this phenomenon. Human requirements propelled by necessities and wants have leveraged heterogeneity deliberately or naively. In the context of engineering materials, light weight heterogeneous materials like composites and cellular solids are outstanding inventions from the last century. The present thesis highlights this phenomenon on a meso-scale to explore generalized variants of circular and elliptical honeycomb structures (HCSs) with an emphasis on their effective transverse elastic responses, a crucial pillar of engineering design and analysis. Homogenized or effective properties are an extension of continuum hypothesis, conceived for ease in analyses. E ective properties are employed in multi-scale analyses resulting in less complex models for analysis, for example, for predicting the speed of wave propogation. The thesis extends and generalizes existing close-packed circular and elliptical HCSs to more broader configurations. Simpler periodic arrangement of the unit cells from numerous exotic possibilities directly incorporates Design for Manufacture and Assembly (DFMA) philosophy and o ers a potential scope for analysis by simpler tools resulting in handy expressions which are of great utility for designer engineers. In this regard, analytical expressions for moduli having compact forms in the case of circular HCS are developed by technical theories and rigorous theory of elasticity. Regression analysis expressions for the moduli of elliptical HCS are presented, and the elasticity solutions for the same are highlighted. The thesis consists of seven chapters with Chapter 1 presenting generalized circular and elliptical HCSs as a potential avenue beyond composite materials. Following a survey of pertinent HCS literature of these HCSs, research gaps and scope are delineated. Chapter 2 briefly y summarizes the ideas, concepts and tools including analytical and numerical methods. This chapter sets the ground for the analysis of generalized circular and elliptical HCS in the following four chapters. Following the classification of the circular HCSs, Chapter 3 assesses the complete transverse elastic responses of generalized circular HCS through technical theories which are a first-order approximation. Here, thin ring theory and the more elaborate curved beam theory are employed as models to assess the moduli. Normal moduli - E and - are obtained by employing Castigliano method, while shear moduli (G ) are obtained by solving the differential equations derived in terms of displacements. Compact expressions for moduli presented wherever possible furnish the designer with a range of moduli for different configurations and modular ratios (Ey=Ex). The results show the range of applicability of technical theories within 5% of FEA. For hexagonal arrays, these results are more refined than those in literature; while the same are new for other configurations. Surprisingly, the more elaborate curved beam theory offers no better results than the thin ring theory. Chapter 4 extends the aforementioned task of assessing the complete trans-verse elastic moduli of generalized circular HCS by employing rigorous theory of elasticity (TOE) which is a second-order approximation. Utilizing Airy stress function in polar coordinates, the boundary value problems resulting from modeling of the circular HCS under different loads are solved analytically in conjunction with FEA employing contact elements. Contact elements circumvent the point loads which give finite values of displacements in technical theories and singular values in TOE. A widely used idea of employing distributed load, statically equivalent to point load, is invoked to empower TOE. The distributed load is assumed a priori and the contact length is obtained from FEA employing con-tact elements. Thus, FEA compliments the present analytical methods. Results demonstrate a very good match between analytical method in conjunction with FEA and numerical results from FEA; the error is within 5% for very thick ring (thickness-radius ratio 0.5). Further, computationally and numerically efficient expressions for displacements give better results with same computational facility. To illustrate the effect of coating on effective moduli, a limited study based on thin ring theory and elasticity theories is undertaken in Chapter 4. The study explores the effects of moduli and thickness ratios of substrate to coating on the effective normal moduli. Employing thin ring theory with only flexure as the bending mode, we get compact expressions giving good match for very thin rings in all confifigurations. The elasticity approach presented for square array demonstrates a very good match with FEA for thick rings. Coatings offer a strategy to increase the effective moduli with same dimensions. Chapter 5 broadens the scope of circular HCS by considering elliptical HCSs. While generalized circular HCS can cater to anisotropic requirement to an extent, larger spectrum is offered by considering elliptical honeycomb structures. In this regard, a generalized version of concentric thin coated elliptical HCS is investigated for transverse moduli. Thin HCSs are explored by technical theories as in circular HCS. However, a lack of exact compact-form expressions necessitates the use of regression analysis. The resulting expressions are presented in terms of ellipticity ratio describing the ovality of the ellipse and geometric parameters. Normal moduli are obtained by Castigliano method implemented in MATHE-MATICA, but shear moduli are obtained from FEA employing beam elements. The need for FEA employing beam elements stems from the subtle fact that Castigliano method implicitly assumes preclusion of rigid body motions, while shear loading for shear moduli evaluation entails rigid body motions. Interestingly, curved beam theory, as in circular HCS, offers no better refinement in assessing the moduli as compared to thin ring theory. The graphs showing the moduli with respect to thickness and modular ratios are presented as design maps to aid the designer. Chapter 6 extends the works of thin concentric coated elliptical to thicker concentric and a novel confocal elliptical HCS, a variant of elliptical HCS. In this regard, thick concentric and confocal elliptical HCS by elasticity approach are attempted for a simple case. Airy stress function in polar coordinates is tried for concentric elliptical HCS. Confocal HCS analysis employs stress function in terms of elliptical coordinate system. After proving the correctness of the stress function for both the cases by comparing the reconstructed boundary conditions with actual boundary conditions, the restrictions in solving the case of rings under load over a small region is highlighted. A parametric study for moduli is under-taken by employing FEA. These are presented as design graphs which compare and contrast the two variants of elliptical HCS on the same graphs. The modular ratio (Ey=Ex) is conspicuously more for confocal elliptical HCS than concentric elliptical HCS. Chapter 7 gives the conclusions in a nutshell, and explores the feasibility of stress evaluation of heterogeneous media on the lines of effective media theory.

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O vidro com composição 2Na2O1CaO3SiO2, sofre nucleação cristalina homogênea em temperaturas entre 450 e 560oC. Os núcleos, essencialmente esféricos, supostamente tem a mesma composição da matriz vítrea. Em amostras amorfas, parcialmente cristalizadas e policristalinas foram feitas medidas de densidade, difratometria de raios-X, analise térmica por calorimetria exploratória de varredura (DSC), medidas ultrasônicas pelo método do pulso-eco, espectroscopias de absorção ótica, infravermelha e Raman. A densidade do vidro é de 2,66 g/cm3 e para amostra policristalina a densidade aumenta para 2,76 g/cm3. O aumento da densidade com o grau de cristalinidade é a causa do aumento das velocidades de propagação de ondas elásticas longitudinal e transversal, e do aumento do numero e da intensidade dos picos nos difratogramas de raios-X. Das medidas de DSC determinamos que a temperatura de transição vítrea ocorre em torno de 40 °C, e calculamos uma entalpia de ativação para a transição vítrea de 78 kcal/mol. Espectros de absorção ótica de amostras com Cr3+ apresentaram o efeito de anti-ressonância Fano, e pequeno deslocamento da banda 4T2 , para energias maiores com o aumento do grau de cristalinidade e em temperaturas baixas (~ 20 K). A partir dos níveis isoenergéticos 2E e 2T1 calculamos o parâmetro de Racah B = 690 cm-1 e a intensidade do campo ligante ? = 10 Dq = 14 840 cm-1. Junto com Cr3+ ocorre o Cr6+ na forma do íon cromato, CrO42-, cujas bandas de absorção estão próximas do ultravioleta, e é responsável pelo efeito Raman pré-ressonante observado. O espectro Raman do vidro é constituído de bandas assimétricas acima de 550 cm-1, e foram decompostas em seis bandas gaussianas. As bandas de maior freqüência foram tentativamente atribuídas à vibrações de tetraedros de sílica com 1 a 4 oxigênios não-ponteantes. Dos espectros Raman reduzidos concluímos que o pico de boson é devido à vibrações dos fônons térmicos o a freqüência da radiação espalhada. Algumas características dos espectros de absorção de amostras com Cr3+ e dos resultados de medidas ultrasônicas foram atribuídas à possível ocorrência de microtensão ou microfissuras na região da interface núcleo-vidro. / Glass with composition 2Na2O1CaO3SiO2, undergoes homogeneous crystal nucleation between 450 and 56OoC. The nuclei are essentially spherical and presumable have the same composition as the glass matrix. Measuriments of density, X-ray diffraction, thermal analysis by differential scanning calorimetry (DSC), ultrasonics by pulse-echo method, optical absorption, infrared and Raman spectroscopy were performed in amorphous, partially crystallized and polycrystalline samples. The density of the glass is 2,66 g/cm3 and 2,76 g/cm3 that of the polycrystalline sample. The increase in density with the degree of crystallinity is the cause of the increasing propagation velocities of longitudinal and transversal elastic waves, and of the increasing peak number and intensities in the X-ray diffractograms. From DSC measurements we determine that the glass transition temperature is about 470o C, and the activation enthalpy for the glass transition was calculated to be 78 kcal/mol. Absorption spectra of Cr3+ containing samples shows the anti-resonance Fano effect, and small displacement of the 4T2 band to higher energies with increasing degree of crystallinity and at lower temperatures (~20 K). From the isoenergetic levels 2E and 2T1 we calculate the Racah parameter B = 690 cm-1 and the ligand field intensity ? = 10 Dq = 14 840 cm-1. Together with Cr3+ occurs Cr6+ as cromate ion, CrO4-2 with absorption bands are near the ultraviolet, and is responsible for the observed pre-resonant Raman effect. The Raman spectrum of the glass is composed of asimetric bands in frequencies above 550 cm-1, which we decompose in six Gaussian shaped bands. The four bands of higher frequencies were tentativily assigned to stretching vibration bond Si-O of silica tetraedra with 1 to 4 non-bridging oxigens. From reduced Raman spectra we concluded that the boson peak is due to thermal phonon vibrations and to the scattered radiation frequency. Some features of absorption spectra of Cr3+ containing glasses and of ultrasonic measurements were assigned to the possible occurence of microtensions or microcracks in the nucleous-glass interf ace region.

O vidro com composição 2Na2O1CaO3SiO2, sofre nucleação cristalina homogênea em temperaturas entre 450 e 560oC. Os núcleos, essencialmente esféricos, supostamente tem a mesma composição da matriz vítrea. Em amostras amorfas, parcialmente cristalizadas e policristalinas foram feitas medidas de densidade, difratometria de raios-X, analise térmica por calorimetria exploratória de varredura (DSC), medidas ultrasônicas pelo método do pulso-eco, espectroscopias de absorção ótica, infravermelha e Raman. A densidade do vidro é de 2,66 g/cm3 e para amostra policristalina a densidade aumenta para 2,76 g/cm3. O aumento da densidade com o grau de cristalinidade é a causa do aumento das velocidades de propagação de ondas elásticas longitudinal e transversal, e do aumento do numero e da intensidade dos picos nos difratogramas de raios-X. Das medidas de DSC determinamos que a temperatura de transição vítrea ocorre em torno de 40 °C, e calculamos uma entalpia de ativação para a transição vítrea de 78 kcal/mol. Espectros de absorção ótica de amostras com Cr3+ apresentaram o efeito de anti-ressonância Fano, e pequeno deslocamento da banda 4T2 , para energias maiores com o aumento do grau de cristalinidade e em temperaturas baixas (~ 20 K). A partir dos níveis isoenergéticos 2E e 2T1 calculamos o parâmetro de Racah B = 690 cm-1 e a intensidade do campo ligante ? = 10 Dq = 14 840 cm-1. Junto com Cr3+ ocorre o Cr6+ na forma do íon cromato, CrO42-, cujas bandas de absorção estão próximas do ultravioleta, e é responsável pelo efeito Raman pré-ressonante observado. O espectro Raman do vidro é constituído de bandas assimétricas acima de 550 cm-1, e foram decompostas em seis bandas gaussianas. As bandas de maior freqüência foram tentativamente atribuídas à vibrações de tetraedros de sílica com 1 a 4 oxigênios não-ponteantes. Dos espectros Raman reduzidos concluímos que o pico de boson é devido à vibrações dos fônons térmicos o a freqüência da radiação espalhada. Algumas características dos espectros de absorção de amostras com Cr3+ e dos resultados de medidas ultrasônicas foram atribuídas à possível ocorrência de microtensão ou microfissuras na região da interface núcleo-vidro. / Glass with composition 2Na2O1CaO3SiO2, undergoes homogeneous crystal nucleation between 450 and 56OoC. The nuclei are essentially spherical and presumable have the same composition as the glass matrix. Measuriments of density, X-ray diffraction, thermal analysis by differential scanning calorimetry (DSC), ultrasonics by pulse-echo method, optical absorption, infrared and Raman spectroscopy were performed in amorphous, partially crystallized and polycrystalline samples. The density of the glass is 2,66 g/cm3 and 2,76 g/cm3 that of the polycrystalline sample. The increase in density with the degree of crystallinity is the cause of the increasing propagation velocities of longitudinal and transversal elastic waves, and of the increasing peak number and intensities in the X-ray diffractograms. From DSC measurements we determine that the glass transition temperature is about 470o C, and the activation enthalpy for the glass transition was calculated to be 78 kcal/mol. Absorption spectra of Cr3+ containing samples shows the anti-resonance Fano effect, and small displacement of the 4T2 band to higher energies with increasing degree of crystallinity and at lower temperatures (~20 K). From the isoenergetic levels 2E and 2T1 we calculate the Racah parameter B = 690 cm-1 and the ligand field intensity ? = 10 Dq = 14 840 cm-1. Together with Cr3+ occurs Cr6+ as cromate ion, CrO4-2 with absorption bands are near the ultraviolet, and is responsible for the observed pre-resonant Raman effect. The Raman spectrum of the glass is composed of asimetric bands in frequencies above 550 cm-1, which we decompose in six Gaussian shaped bands. The four bands of higher frequencies were tentativily assigned to stretching vibration bond Si-O of silica tetraedra with 1 to 4 non-bridging oxigens. From reduced Raman spectra we concluded that the boson peak is due to thermal phonon vibrations and to the scattered radiation frequency. Some features of absorption spectra of Cr3+ containing glasses and of ultrasonic measurements were assigned to the possible occurence of microtensions or microcracks in the nucleous-glass interf ace region.