L'objectif principal de cette thèse est de développer un modèle numérique capable de proposer une représentation fine des phénomènes de fissuration pour les matériaux quasi-fragiles à matrice cimentaire. Dans ce sens, l'échelle pertinente retenue est l'échelle mesoscopique. L'échelle mesoscopique est ici de l'ordre du centimètre et le matériau peut être considéré comme bi-phasique (agrégats inclus dans un mortier, contenant lui même des inclusions de taille inférieure). Par ailleurs, de part la diversité des phénomènes de fissuration pour les matériaux quasi-fragiles comme le béton, il est nécessaire de mettre en place un modèle capable de représenter explicitement les fissures à l'interface agrégats/mortier et/ou dans n'importe quelles des deux phases (agrégats et mortier). La modélisation numérique des phénomènes de fissuration proposée s'inscrit, ici, dans le cadre de la méthode des éléments finis à discontinuité forte. Plus précisément, la fissure est ici définie comme l'apparition d'une discontinuité de déplacements ou encore d'une zone d'épaisseur nulle dans laquelle toutes les déformations sont localisées. Elle correspond au cas extrême des bandes de localisation observées dans les sols ou les roches avec une largeur des bandes tendant vers zéro. Par ailleurs, le modèle proposé intégre aussi une discontinuité faible (discontinuité de déformations) afin de capturer les hétérogénéités sans que le maillage soit contraint. Finalement le but est d'intégrer ce meso-modèle dans le cadre d'une approche multi-échelle séquencée permettant le transfert des informations du niveau mesoscopique vers le niveau macroscopique ou au moins sa borne inférieure, le Volume élémentaire Représentatif. Cette approche séquencée permet, par exemple, de déterminer une surface de rupture macroscopique (dans l'esprit d'une fonction seuil) intégrant les principales caractéristiques des matériaux cimentaires. / The main goal of this work is to develop a numerical model capable of providing a fine representation of cracks phenomenon in the case of quasi-brittle material such as concrete. In that way, the relevant chosen scale is the mesoscopic one. The order of magnitude of this scale is here tehe centimeter and the material can be considered as a two-phase material (aggregates melt into a mortar matrix). In addition, due to the diversity of cracks phenomenon in concrete like-material, it is necessary to introduce a model able to explicitely represent cracks at the interface aggregates/mortar matrix and/or in any of the two phases. The numerical cracks phenomenon modeling proposed in this work is cast in the framework of the finite element method with strong discontinuity. Moreover, the proposed model takes into account a weak discontinuity in order to capture heterogeneities without a mesh constrained by the phyysical interfaces between the aggregates and the mortar matrix. Finally, the aim is to use this meso-model in the framework of a sequential multi-scale approach which allows to transfer information from the meso-scale toward the macro-scale.

The propagation of light beams in inhomogeneous dielectric media is considered. The derivation begins with first principles and remains general enough to include off-axis asymmetric multimode input beams in tapered lenslike media with spatial variations of gain or loss. The tapering of lenslike media leads to a number of important applications. A parabolic taper is proposed as a model for a heated axially stretched fiber taper, and beams in such media are fully characterized. Other models are proposed by the concatenation of a parabola with other taper functions.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 160-166).

This dissertation research focuses on micromechanical modeling and simulations of two-phase heterogeneous materials exhibiting anisotropic and non-uniform microstructures with long-range spatial correlations. Completed work involves development of methodologies for realistic micromechanical analyses of materials using a combination of stereological techniques, two- and three-dimensional digital image processing, and finite element based modeling tools. The methodologies are developed via its applications to two technologically important material systems, namely, discontinuously reinforced aluminum composites containing silicon carbide particles as reinforcement, and boron modified titanium alloys containing in situ formed titanium boride whiskers. Microstructural attributes such as the shape, size, volume fraction, and spatial distribution of the reinforcement phase in these materials were incorporated in the models without any simplifying assumptions. Instrumented indentation was used to determine the constitutive properties of individual microstructural phases. Micromechanical analyses were performed using realistic 2D and 3D models and the results were compared with experimental data. Results indicated that 2D models fail to capture the deformation behavior of these materials and 3D analyses are required for realistic simulations. The effect of clustering of silicon carbide particles and associated porosity on the mechanical response of discontinuously reinforced aluminum composites was investigated using 3D models. Parametric studies were carried out using computer simulated microstructures incorporating realistic microstructural attributes. The intrinsic merit of this research is the development and integration of the required enabling techniques and methodologies for representation, modeling, and simulations of complex geometry of microstructures in two- and three-dimensional space facilitating better understanding of the effects of microstructural geometry on the mechanical behavior of materials.

Thesis (Ph. D.)--University of Oregon, 1999. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 165-166). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9948028.

Functionally graded materials (FGMs) are composites that have continuously varying material properties, which eliminate undesirable stress concentrations that might otherwise occur in layered composites. The concept of inhomogeneously varying properties is observed in nature; examples include bones, teeth, shells and timber. Modern engineering applications of FGMs include thermal barrier coatings, wear-resistant coatings, biomedical implants and MEMS devices. Syntactic foams, particle filled nano-composites are examples of inhomogeneous materials of current interest. Analyses and experiments available in the literature have focused on characterizing the inhomogeneous material modulus and density variations. Common techniques employed are nano-indentation and wave propagation studies. There are a few fracture mechanics analyses and experiments available in the literature; most of which are devoted to measuring the fracture toughness of graded materials. A few fracture analyses of graded materials are devoted to deriving asymptotic stress, strain and displacement fields around stationary and steadily growing cracks in inhomogeneous materials. Only a few studies exist that deal with understanding the effect of material property inhomogeneity on the spontaneous crack propagation. In the present thesis the effect of material property inhomogeneity on the dynamic fracture mechanics of cracks in FGMs is described. Numerical analysis of the elastodynamic initial boundary value problem is performed using a spectral scheme. Spectral scheme is a special numerical technique developed to simulate spontaneous, planar crack propagation in a variety of materials. The method is numerically efficient as it can be implemented on parallel machines with ease. The numerical scheme is versatile and can handle any state-and rate-dependent traction-separation laws (cohesive zone models) or frictional laws. Spectral scheme has successfully been used in simulating intersonic crack propagation, earthquake slip dynamics and also direct silicon wafer bonding process used in realizing 3D MEMS structures. In the present work, the spectral formulation accounts for the inhomogeneous variation in the material wave speeds in the medium. The effect of inhomogeneity on spontaneous crack propagation due to in-plane mixed-mode loading is also addressed here. A parametric study has been performed by varying the inhomogeneity length scales independently in the top and bottom half-spaces. The effect of inhomogeneity in shear wave speed on the dynamic stress intensity factors (SIFs) of a crack propagating in a quasi-steady-state along the interface between the two functionally graded half-spaces is studied. A symmetric hardening FGM offers the maximum fracture resistance, while the fracture resistance is minimum for a symmetric softening FGM. Our simulation shows that increasing the inhomogeneity in the wave speed leads to eliminate the overshoot in the dynamic stress intensity factor. The magnitude of the steady-state (long-time) SIF increases indicating an increase in the fracture resistance. The effect of the inhomogeneous wave speed on the mode-3 crack propagation characteristics is demonstrated by taking snapshots of the crack opening at a time interval. The magnitude of the crack sliding displacement is found to increase with increase in the inhomogeneity. The effect of the material property inhomogeneity on the mode-1 crack propagation is simulated to track the crack opening displacements. The inhomogeneity is assumed to be symmetric about the weak-plane. Our spectral scheme developed here for functionally graded material with exponential variation in the material properties is capable of simulating independent bimaterial combinations. When the graded material becomes progressively stiffer and denser (hardening), the crack opening displacement in reduced, indicating an increase in the fracture resistance. On the other hand, for the softening FGMs the crack opening displacement increases indicating a reduction in fracture toughness. It is noted that the cohesive fracture resistance on the weak-plane remains same in all the FGMs.

Ce travail concerne l’étude acoustique théorique et expérimentale des matériaux poreux à squelette métallique, macroscopiquement homogènes et inhomogènes ainsi que l’étude de leurs propriétés mécaniques de comportement au choc pour comparaison. Le modèle acoustique de Johnson -Champoux - Allard s’est montré adapté pour la modélisation acoustique. Ce modèle associé à une approche proposée récemment et utilisant le concept de matrices de transfert en parallèle a permis, dans une nouvelle approche basée sur les “mélanges de matériaux”, d’étudier les matériaux poreux macroscopiquement inhomogènes. Par ailleurs, une étude paramétrique du coefficient d’absorption en fonction de la porosité et de la fréquence a été proposée. Les maxima d’absorption ainsi que l’enveloppe des courbes d’absorption en fonction de la porosité ont été étudiés. En premier lieu, un matériau théorique à propriétés indépendantes a été étudié. Les matériaux réels à propriétés interdépendantes ont ensuite été abordés à l’aide d’un modèle reliant leurs propriétés à la porosité. Enfin, une comparaison entre les propriétés acoustiques et les propriétés mécaniques de comportement à l’impact a été initiée en vue de déterminer un critère objectif permettant de proposer un compromis entre les deux domaines. / This work is concerned with the theoretical and experimental study of the acoustical properties of macroscopically homogenous and inhomogeneous porous media as well as their mechanical response to impacts. The model of Johnson - Champoux - Allard appeared adapted for the acoustical modeling. This model, associated with a recently developed approach involving the concept of parallel transfer matrices has lead to a new approach of macroscopically inhomogeneous porous materials based on “mixtures of materials”. Furthermore, a parametric study of the absorption coefficient as a function of porosity and frequency has been proposed. The maximums of absorption as well as the envelop of the absorption curves have been studied as functions of porosity. First, a theoretical material with independent parameters has been studied. Real materials with nonindependent parameters were then investigated with the help of a model relating their properties to the porosity. Finally, a comparison between the acoustical and mechanical properties has been initiated in view of determining an objective criterion that will allow to propose a trade off between the two fields.

This thesis considers the problem of determining Casimir-Lifshitz forces in inhomogeneous media. The ground-state energy of the electromagnetic field in a piston-geometry is discussed. When the cavity is empty, the Casimir pressure on the piston is finite and independent of the small-scale physics of the media that compose the mirrors. However, it is demonstrated that, when the cavity is filled with an inhomogeneous dielectric medium, the Casimir energy is cut-off dependent. The local behavior of the stress tensor commonly used in calculations of Casimir forces is also determined. It is shown that the usual expression for the stress tensor is not finite anywhere within such a medium, whatever the temporal dispersion or index profile, and that this divergence is unlikely to be removed by modifying the regularisation. These findings suggest that the value of the Casimir pressure may be inextricably dependent on the detailed behavior of the mirror and the medium at large wave vectors. This thesis also examines two exceptions to this rule: first, the case of an idealised metamaterial is considered which, when introduced into a cavity, reduces the magnitude of the Casimir force. It is shown that, although the medium is inhomogeneous, it does not contribute additional scattering events but simply modifies the effective length of the cavity, so the predicted force is finite and can be stated exactly. Secondly, a geometric argument is presented for determining a Casimir stress in a spherical mirror filled with the inhomogeneous medium of Maxwell's fish-eye. This solution questions the idea that the Casimir force of a spherical mirror is repulsive, but prompts additional questions concerning regularisation and the role of non-local effects in determining Casimir forces.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 166-181).

The macroscopic behavior of complex heterogeneous materials is strongly governed by the interactions between their elementary constituents within their microstructure. Beside experimental efforts characterizing the behaviors of such materials, there is growing interest, in view of the increasing computational power available, in building models representing their microstructural systems integrating the elementary behaviors of their constituents and their geometrical organization. While a large number of contributions on this aspect focus on the investigation of advanced physics in material parameter studies using rather simple geometries to represent the spatial organization of heterogeneities, few are dedicated to the exploration of the role of microstructural geometries by means of morphological parameter studies.<p>The critical ingredients of this second type of investigation are (I) the generation of sets of representative volume elements ( RVE ) describing the geometry of microstructures with a satisfying control on the morphology relevant to the material of interest and (II) the discretization of governing equations of a model representing the investigated physics on those RVEs domains. One possible reason for the under-representation of morphologically detailed RVEs in the related literature may be related to several issues associated with the geometrical complexity of the microstructures of considered materials in both of these steps. Based on this hypothesis, this work is aimed at bringing contributions to advanced techniques for the generation and discretization of microstructures of complex heterogeneous materials, focusing on geometrical issues. In particular, a special emphasis is put on the consistent geometrical representation of RVEs across generation and discretization methodologies and the accommodation of a quantitative control on specific morphological features characterizing the microstructures of the covered materials.<p>While several promising recent techniques are dedicated to the discretization of arbitrary complex geometries in numerical models, the literature on RVEs generation methodologies does not provide fully satisfying solutions for most of the cases. The general strategy in this work consisted in selecting a promising state-of-the-art discretization method and in designing improved RVE generation techniques with the concern of guaranteeing their seamless collaboration. The chosen discretization technique is a specific variation of the generalized / extended finite element method that accommodates the representation of arbitrary input geometries represented by level set functions. The RVE generation techniques were designed accordingly, using level set functions to define and manipulate the RVEs geometries. <p>The RVE methodologies developed are mostly morphologically motivated, incorporating governing parameters allowing the reproduction and the quantitative control of specific morphological features of the considered materials. These developments make an intensive use of distance fields and level set functions to handle the geometrical complexity of microstructures. Valuable improvements were brought to the RVE generation methodologies for several materials, namely granular and particle-based materials, coated and cemented geomaterials, polycrystalline materials, cellular materials and textile-based materials. RVEs produced using those developments have allowed extensive testing of the investigated discretization method, using complex microstructures in proof-of-concept studies involving the main ingredients of RVE-based morphological parameter studies of complex heterogeneous materials. In particular, the illustrated approach offers the possibility to address three crucial aspects of those kinds of studies: (I) to easily conduct simulations on a large number of RVEs covering a significant range of morphological variations for a material, (II) to use advanced constituent material behaviors and (III) to discretize large 3D RVEs. Based on those illustrations and the experience gained from their realization, the main strengths and limitations of the considered discretization methods were clearly identified. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished