Thesis (Ph. D.)--Oregon State University, 2001. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

In this thesis, we have investigated some interesting dynamical problems in microstructural continuum using Eringen's polar theory. These problems are pertaining to surface waves in a microstretch plate, Stoneley waves at an interface between two different microstretch half-spaces, surface waves in a micropolar cylindrical borehole filled with micropolar fluid, reflection and transmission of elastic waves at a liquid/solid half-space and reflection of elastic waves from a micropolar mixture porous half-space.

This work is concerned with the theoretical development of dynamic equations for gyroelastic systems which are dynamic systems with four basic types of continuous mechanical influences, i.e. inertia, elasticity, damping, and gyricity or stored angular momentum. Assuming unrestricted or large attitude changes for the axes of the gyros and utilizing two different theories of elasticity, i.e. the classical and micropolar theories of elasticity, the energy expressions and equations of motion for the undamped classical and micropolar gyroelastic continua are derived. Whereas the micropolar gyroelastic continuum model with extra coefficients and degrees of freedom is primarily developed to account for the asymmetric elasticity, it also proves itself to be more comprehensive in describing the actual gyroscopic system or structure. The dynamic equations of the general three-dimensional gyroelastic continua are reduced to the case of a one-dimensional gyroelastic continua in the three-dimensional space, i.e. three-dimensional gyrobeams. Two different gyrobeam models are developed, one based on the classical beam torsion and bending theories and one based on the simplified micropolar beam torsion and bending theories. Finite element models corresponding to the classical and micropolar gyrobeams are built in MATLAB and used for numerical analysis. The classical and micropolar gyrobeam models are analyzed and compared, against the earlier gyrobeam models developed by other authors and also against each other, through numerical examples. It is shown that there are significant differences between the developed unrestricted classical gyrobeam model and the previously derived zero-order restricted classical gyrobeam models. These differences are more pronounced in the shorter beams and for the transverse gyricity case. The results also indicate that the unrestricted classical and micropolar gyrobeam models behave very diversely in a wide range of micropolar elastic constants even where the classical and micropolar elasticity models coincide. As a foundation for development of the above-mentioned theories, the correct approach for simplification of the micropolar elasticity to the classical elasticity, the simple torsion and bending theories for micropolar beams, and the correct approximation of infinitesimal rotations or microrotations are derived and presented.

The term “granular material” describes any assembly of macroscopic particles. This broad definition encompasses a wide variety of everyday materials, for example sand, cereals, gravel and powders. However, despite their commonplace nature, to date no universally accepted set of constitutive equations exists to describe the behaviour of these materials. Thermomechanics and micromechanics are two modelling methodologies previously employed in separate efforts to represent granular behaviour. In this thesis, the two theories are integrated to develop new models of idealised granular materials. (For complete abstract open document)

Thesis (Ph. D.)--Oregon State University, 1992. / Typescript (photocopy). Includes bibliographical references (leaves 106-113). Also available on the World Wide Web.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / O objetivo desse trabalho à estudarmos a controlabilidade aproximada, via estratÃgia de Stackeberg-Nash, para equaÃÃo do calor em domÃnios ilimitados, bem como para equaÃÃo da onda e para fluidos micropolares em domÃnios com fronteira variÃvel . / The purpose of this work is study the approximate controllability, via Stackelberg-Nash strategies to heat equation in unlimited domains, as well to wave equation and for micropolars fluids in domains with moving boundary.

La réparation de l’humain est un secteur d’activité qui nécessite les compétences en sciences médicales et sciences dites «dures». Dans de nombreux cas, tout ou partie d’un organe doit être remplacé par un substitut en matériau inerte. C’est par exemple le cas en implantologie où l’on s’intéresse au remplacement de dents. La pose d’un implant dentaire est un acte chirurgical qui consiste à introduire dans l’os de la mandibule un dispositif en matériau inerte destiné à recevoir la couronne dentaire. Ces prothèses sont plus ou moins tolérées par l’organisme vivant (environ 5% de rejet) et peuvent dans certains cas conduire à une ruine de l’os ou engendrer des infections connues sous le nom de péri-implantite. Pour améliorer la biocompatibilité de ces dispositifs médicaux, plusieurs pistes sont explorées. On peut s’intéresser à la géométrie de l’implant et son état de surface, au matériau de l’implant ou bien au système mécanique implant-os. C’est dans ce dernier cadre que nous avons situé notre travail de thèse. Le système os/dent est un système mécanique soumis à des sollicitations répétées de forte intensité. Les niveaux de contrainte et de déformation atteints lors de la mastication participent à la stabilité de l’ensemble et la viabilité de ces milieux vivants. Ces niveaux de contrainte et de déformation doivent être reproduits dans l’os dans le cas du système implant-os. On espère ainsi assurer la viabilité de l’os et éviter les divers processus de dégradation. Il convient donc de simuler et analyser la réponse d’un tel système à des sollicitations mécaniques. Ce travail nécessite la modélisation du comportement de l’os et de l’implant. Ce dernier est considéré comme un matériau métallique classique sollicité dans son domaine de déformation élastique. Pour ce qui est l’os, son observation fine révèle sa nature multi-échelle et nous avons choisi de modéliser son comportement par une particularisation du milieu micromorphique de Eringen. Plus précisément nous l’avons considéré comme un milieu élastique micropolaire. Pour résoudre les équations de champs du problème, il a été nécessaire de développer un outil numérique spécifiquement dédié. Cet outil est basé sur une combinaison astucieuse de la méthode des éléments de frontières et d’une méthode sans maillage (meshless), plus précisément une méthode de collocation par points. Dans un premier temps, afin de comprendre le principe de la méthode, nous avons développé l’outil numérique pour résoudre une équation de champ scalaire, ici équation de la conduction thermique transitoire. Nous avons pu constater l’efficacité de la méthode pour des systèmes en trois dimensions. Dans un second temps nous avons adapté notre méthode numérique pour résoudre des équations de champ vectoriel qui sont dans notre cas les équations pour les milieux élastiques micropolaires. L’outil numérique a été validé sur un nombre d’exemples possédant une solution analytique ou en comparaison aux résultats de la littérature sur d’autres types de problèmes. L’outil a ensuite été appliqué à l’analyse du système implant-os. Pour comprendre l’apport de la microstructure d’un milieu élastique micropolaire, en comparaison à un milieu élastique classique, nous avons fait différentes études du système implant-os sous sollicitations mécaniques diverses en considérant les deux types de modélisation pour l’os. Les paramètres macroscopiques pour un milieu élastique micropolaire sont les mêmes que pour un milieu élastique classique. Les différences obtenues ne proviendront que de l’apport de la microstructure. Les résultats obtenus montrent que la modélisation fine du comportement mécanique adoptée pour l’os est réaliste au regard des contraintes induites par la sollicitation et à la diminution notable des sauts de contraintes à l’interface os/métal comparé au cas de la modélisation de l’os comme un milieu élastique classique. Ces résultats ont d’ores et déjà permis de comprendre certaines observations cliniques. / The repair of the human is a sector of activity which requires skills in medical sciences and sciences known as "hard". In many cases, all or part of an organ must be replaced by a substitute made of inert material. This is for example the case in implantology where one is interested in the replacement of teeth. The installation of a dental implant is a surgical act which consists in introducing into the bone of the mandible a device made of inert material intended to receive the dental crown. These prostheses are more or less tolerated by the living organism (about 5% of rejection) and can in some cases lead to a bone ruin or cause infections known as peri-implantitis. To improve the biocompatibility of these medical devices, several tracks are explored. We can focus on the geometry of the implant and its surface condition, the material of the implant or the mechanical bone / implant system. It is in this last frame that we located our work of thesis. The bone / tooth system is a mechanical system subject to repeated intense stress. The levels of stress and deformation achieved during chewing contribute to the overall stability and viability of these living media. These stress and strain levels must be reproduced in the bone in the case of the bone / implant system. It is hoped to ensure the viability of the bone and to avoid the various processes of degradation. It is therefore necessary to simulate and analyze the response of such a system to mechanical stresses. This work requires modeling the behavior of the bone and the implant. The latter is considered as a conventional metallic material stressed in its field of elastic deformation. As for the bone, its fine observation reveals its multi-scale nature and we have chosen to model its behavior by a particularization of Eringen's micromorphic environment. More precisely we have considered it as a micropolar elastic medium. To solve the field equations of the problem, it was necessary to develop a dedicated digital tool. This tool is based on a clever combination of the boundary element method and a meshless method, more precisely a collocation method. At first, in order to understand the principle of the method, we developed the numerical tool to solve a scalar field equation, here equation of transient thermal conduction. We have seen the effectiveness of the method for three-dimensional systems. In a second time we adapted our numerical method to solve vector field equations which are in our case the equations for the micropolar elastic media. The digital tool has been validated on a number of examples having an analytical solution or in comparison with the results of the literature. The digital tool was then applied to the analysis of the bone / implant system. To understand the contribution of the microstructure of a micropolar elastic medium, compared to a conventional elastic medium, we made different studies of the implant / bone system under various mechanical stress considering both types of modeling for the bone. The macroscopic parameters for a micropolar elastic medium are the same as for a conventional elastic medium. The differences obtained will come only from the contribution of the microstructure. The results obtained show that the fine modeling of the mechanical behavior adopted for the bone is realistic with regard to the stresses induced by the stress and to the noticeable decrease of the stress jumps at the bone / metal interface compared to the case of the modeling of the equivalent classic elastic medium. These results have already made it possible to understand certain clinical observations.

The goal of this research is to develop a robust, continuum-based approach for a three-dimensional, Finite Element Method (FEM) simulation of layered geomaterials. There are two main approaches to the numerical modeling of layered geomaterials; discrete or discontinuous techniques and an equivalent continuum concept. In the discontinuous methodology, joints are explicitly simulated. Naturally, discrete techniques provide a more accurate description of discontinuous materials. However, they are complex and necessitate care in modeling of the interface. Also, in many applications, the definition of the input model becomes impractical as the number of joints becomes large. In order to overcome the difficulties associated with discrete techniques, a continuum-based approach has become popular in some application areas. When using a continuum model, a discrete material is replaced by a homogenized continuous material, also known as an 'equivalent continuum'. This leads to a discretization that is independent of both the orientation and spacing of layer boundaries. However, if the layer thickness (i.e., internal length scale of the problem) is large, the classical continuum approach which neglects the effect of internal characteristic length can introduce large errors into the solution. In this research, a full 3D FEM formulation for the elasto-plastic modeling of layered geomaterials is proposed within the framework of Cosserat theory. The effect of the bending stiffness of the layers is incorporated in the matrix of elastic properties. Also, a multi-surface plasticity model, which allows for plastic deformation of both the interfaces between the layers and intact material, is introduced. The model is verified against analytical solutions, discrete numerical models, and experimental data. It is shown that the FEM Cosserat formulation can achieve the same level of accuracy as discontinuous models in predicting the displacements of a layered material with a periodic microstructure. Furthermore, the method is capable of reproducing the strength behaviour of materials with one or more sets of joints. Finally, due to the incorporation of layer thickness into the constitutive model, the FEM Cosserat formulation is capable of capturing complicated failure mechanisms such as the buckling of individual layers of material which occur in stratified media.

The goal of this research is to develop a robust, continuum-based approach for a three-dimensional, Finite Element Method (FEM) simulation of layered geomaterials. There are two main approaches to the numerical modeling of layered geomaterials; discrete or discontinuous techniques and an equivalent continuum concept. In the discontinuous methodology, joints are explicitly simulated. Naturally, discrete techniques provide a more accurate description of discontinuous materials. However, they are complex and necessitate care in modeling of the interface. Also, in many applications, the definition of the input model becomes impractical as the number of joints becomes large. In order to overcome the difficulties associated with discrete techniques, a continuum-based approach has become popular in some application areas. When using a continuum model, a discrete material is replaced by a homogenized continuous material, also known as an 'equivalent continuum'. This leads to a discretization that is independent of both the orientation and spacing of layer boundaries. However, if the layer thickness (i.e., internal length scale of the problem) is large, the classical continuum approach which neglects the effect of internal characteristic length can introduce large errors into the solution. In this research, a full 3D FEM formulation for the elasto-plastic modeling of layered geomaterials is proposed within the framework of Cosserat theory. The effect of the bending stiffness of the layers is incorporated in the matrix of elastic properties. Also, a multi-surface plasticity model, which allows for plastic deformation of both the interfaces between the layers and intact material, is introduced. The model is verified against analytical solutions, discrete numerical models, and experimental data. It is shown that the FEM Cosserat formulation can achieve the same level of accuracy as discontinuous models in predicting the displacements of a layered material with a periodic microstructure. Furthermore, the method is capable of reproducing the strength behaviour of materials with one or more sets of joints. Finally, due to the incorporation of layer thickness into the constitutive model, the FEM Cosserat formulation is capable of capturing complicated failure mechanisms such as the buckling of individual layers of material which occur in stratified media.

In this thesis, the two-dimensional, transient, laminar flow of viscous and incompressible fluids is solved by using the dual reciprocity boundary element method (DRBEM). Natural convection and mixed convection flows are also solved with the addition of energy equation. Solutions of natural convection flow of nanofluids and micropolar fluids in enclosures are obtained for highly large values of Rayleigh number. The fundamental solution of Laplace equation is used for obtaining boundary element method (BEM) matrices whereas all the other terms in the differential equations governing the flows are considered as nonhomogeneity. This is the main advantage of DRBEM to tackle the nonlinearities in the equations with considerably small computational cost. All the convective terms are evaluated by using the DRBEM coordinate matrix which is already computed in the formulation of nonlinear terms. The resulting systems of initial value problems with respect to time are solved with forward and central differences using relaxation parameters, and the fourth-order Runge-Kutta method. The numerical stability analysis is developed for the flow problems considered with respect to the choice of the time step, relaxation parameters and problem constants. The stability analysis is made through an eigenvalue decomposition of the final coefficient matrix in the DRBEM discretized system. It is found that the implicit central difference time integration scheme with relaxation parameter value close to one, and quite large time steps gives numerically stable solutions for all flow problems solved in the thesis. One-and-two-sided lid-driven cavity flow, natural and mixed convection flows in cavities, natural convection flow of nanofluids and micropolar fluids in enclosures are solved with several geometric configurations. The solutions are visualized in terms of streamlines, vorticity, microrotation, pressure contours, isotherms and flow vectors to simulate the flow behaviour.