GUIMARÃES, Anderson Vieira. Mecanismos de fratura em materiais multifásicos. 2014. 75 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2014-08-29T19:55:57Z No. of bitstreams: 1 2014_dis_avguimaraes.pdf: 11579215 bytes, checksum: f6245c912d49cbd6300b532985e1ab7d (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2014-08-29T20:31:04Z (GMT) No. of bitstreams: 1 2014_dis_avguimaraes.pdf: 11579215 bytes, checksum: f6245c912d49cbd6300b532985e1ab7d (MD5) / Made available in DSpace on 2014-08-29T20:31:04Z (GMT). No. of bitstreams: 1 2014_dis_avguimaraes.pdf: 11579215 bytes, checksum: f6245c912d49cbd6300b532985e1ab7d (MD5) Previous issue date: 2014 / The understanding about the fractures processes in materials has a big importance for physics and civil construction industries. Through the fractures processes, we can better understand the materials’ elastics properties as its macroscopic Young module, rupture tension and rigidity module. We can define the fractures processes as those which divide a system into two or more parts, destroying the global connection of the elements that constitute it. In this context, in the first chapter, we can find a mathematical description of continuum mechanics equations. The second chapter discusses the model of Discrete Element(DEM), which is a numerical method capable of describing the mechanical behavior of granular materials. In the third chapter, we built the computational model for studying the mechanicals properties of three types of samples, crystalline, amorphous and multiphase. The computational model showed itself quite interesting and presented results which we can consider satisfactory. / O entendimento sobre os processos de fraturas em materiais é de grande importância para a física e indústrias da construção civil. Através dos processos de fraturas podemos compreender melhor as propriedades elásticas dos materiais, como seu módulo de Young macroscópico, tensão de ruptura e módulo de rigidez. Podemos definir os processos de fraturas como sendo aqueles que dividem um sistema em duas ou mais partes, destruindo a conexão global dos elementos que o constituem. Nesse contexto, no primeiro capítulo é feito uma descrição matemática das equações da mecânica do contínuo, no segundo capítulo aborda-se o modelo de elementos discretos (DEM) que é um método numérico capaz de descrever o comportamento mecânico de materiais granulados. No terceiro capítulo, construímos o modelo computacional para estudar, as propriedades mecânicas de 3 tipos de amostras, cristalina, amorfa e multifásica. O modelo computacional utilizado se mostrou bastante interessante e apresentou resultados que podemos considerar como sendo satisfatórios.

In this thesis we analyze the buckling behavior of an infinitely long, thin, uniform, inextensible, elastic plate that has a steady current flowing along its length. We are concerned with the derivation of the nonlinear equations of motion using nonlinear continuum mechanics, and subsequent analysis of the buckling behavior of the plate under electromagnetic self-forces. In particular, we concentrate on how the body-forces that result from the applied current determine the buckled configurations. We derive both analytical and numerical results, and in the process develop a novel boundary value problem solver for integro-differential equations in addition to a predictor-corrector algorithm to continue solutions with respect to the control parameters. We take a relatively complex problem in magneto-solid mechanics and elasticity theory and form a realistic model that sheds light on the bifurcation and buckling behavior resulting from the electromagnetic-field- induced self-forces that are derived in their full, exact form using Biot-Savart Law. / Ph. D.

In this dissertation, an innovative approach combining continuum mechanics and atomistic simulations is exposed to develop a nanomechanics theory for modeling and predicting the macroscopic behavior of nanomaterials. This nanomechanics theory exhibits the simplicity of the continuum formulation while taking into account the discrete atomic structure and interaction near surfaces/interfaces. There are four primary objectives to this dissertation. First, theory of interfaces is revisited to better understand its behavior and effects on the overall behavior of nanostructures. Second, atomistic tools are provided in order to efficiently determine the properties of free surfaces and interfaces. Interface properties are reported in this work, with comparison to both theoretical and experimental characterizations of interfaces. Specifically, we report surface elastic properties of groups 10 11 transition metals as well as properties for low-CSL grain boundaries in copper. Third, we propose a continuum framework that casts the atomic level information into continuum quantities that can be used to analyze, model and simulate macroscopic behavior of nanostructured materials. In particular, we study the effects of surface free energy on the effective modulus of nano-particles, nanowires and nano-films as well as nanostructured crystalline materials and propose a general framework valid for any shape of nanostructural elements / nano-inclusions (integral forms) that characterizes the size-dependency of the elastic properties. This approach bridges the gap between discrete systems (atomic level interactions) and continuum mechanics. Finally this continuum outline is used to understand the effects of surfaces on the overall behavior of nano-size structural elements (particles, films, fibers, etc.) and nanostructured materials. More specifically we will discuss the impact of surface relaxation, surface elasticity and non-linearity of the underlying bulk on the properties nanostructured materials.

O entendimento sobre os processos de fraturas em materiais à de grande importÃncia para a fÃsica e indÃstrias da construÃÃo civil. AtravÃs dos processos de fraturas podemos compreender melhor as propriedades elÃsticas dos materiais, como seu mÃdulo de Young macroscÃpico, tensÃo de ruptura e mÃdulo de rigidez. Podemos definir os processos de fraturas como sendo aqueles que dividem um sistema em duas ou mais partes, destruindo a conexÃo global dos elementos que o constituem. Nesse contexto, no primeiro capÃtulo à feito uma descriÃÃo matemÃtica das equaÃÃes da mecÃnica do contÃnuo, no segundo capÃtulo aborda-se o modelo de elementos discretos (DEM) que à um mÃtodo numÃrico capaz de descrever o comportamento mecÃnico de materiais granulados. No terceiro capÃtulo, construÃmos o modelo computacional para estudar, as propriedades mecÃnicas de 3 tipos de amostras, cristalina, amorfa e multifÃsica. O modelo computacional utilizado se mostrou bastante interessante e apresentou resultados que podemos considerar como sendo satisfatÃrios. / O entendimento sobre os processos de fraturas em materiais à de grande importÃncia para a fÃsica e indÃstrias da construÃÃo civil. AtravÃs dos processos de fraturas podemos compreender melhor as propriedades elÃsticas dos materiais, como seu mÃdulo de Young macroscÃpico, tensÃo de ruptura e mÃdulo de rigidez. Podemos definir os processos de fraturas como sendo aqueles que dividem um sistema em duas ou mais partes, destruindo a conexÃo global dos elementos que o constituem. Nesse contexto, no primeiro capÃtulo à feito uma descriÃÃo matemÃtica das equaÃÃes da mecÃnica do contÃnuo, no segundo capÃtulo aborda-se o modelo de elementos discretos (DEM) que à um mÃtodo numÃrico capaz de descrever o comportamento mecÃnico de materiais granulados. No terceiro capÃtulo, construÃmos o modelo computacional para estudar, as propriedades mecÃnicas de 3 tipos de amostras, cristalina, amorfa e multifÃsica. O modelo computacional utilizado se mostrou bastante interessante e apresentou resultados que podemos considerar como sendo satisfatÃrios. / The understanding about the fractures processes in materials has a big importance for physics and civil construction industries. Through the fractures processes, we can better understand the materialsâ elastics properties as its macroscopic Young module, rupture tension and rigidity module. We can define the fractures processes as those which divide a system into two or more parts, destroying the global connection of the elements that constitute it. In this context, in the first chapter, we can find a mathematical description of continuum mechanics equations. The second chapter discusses the model of Discrete Element(DEM), which is a numerical method capable of describing the mechanical behavior of granular materials. In the third chapter, we built the computational model for studying the mechanicals properties of three types of samples, crystalline, amorphous and multiphase. The computational model showed itself quite interesting and presented results which we can consider satisfactory. / The understanding about the fractures processes in materials has a big importance for physics and civil construction industries. Through the fractures processes, we can better understand the materialsâ elastics properties as its macroscopic Young module, rupture tension and rigidity module. We can define the fractures processes as those which divide a system into two or more parts, destroying the global connection of the elements that constitute it. In this context, in the first chapter, we can find a mathematical description of continuum mechanics equations. The second chapter discusses the model of Discrete Element(DEM), which is a numerical method capable of describing the mechanical behavior of granular materials. In the third chapter, we built the computational model for studying the mechanicals properties of three types of samples, crystalline, amorphous and multiphase. The computational model showed itself quite interesting and presented results which we can consider satisfactory.

Call number: LD2668 .T4 1985 K57 / Master of Science

The general principles of continuum mechanics such as conservation of mass, conservation of momenta, first and second law of thermodynamics are applicable to all materials irrespective of their internal constitutions. These principles alone do not provide sufficient equations to obtain solutions for any boundary value problems. The additional equations are provided by the constitutive laws. There are many groups of constitutive theories. Of them, the theory of plasticity describes rate independent nonlinear and inelastic behavior of materials. A plasticity-based constitutive law is proposed herein for geological materials. The model, however, may also be used for other frictional materials. A generalized approach is followed in formulating the proposed constitutive model. The technique can be used to construct plasticity-based constitutive models for any other materials. A series of laboratory tests are performed on cubical soil specimens using a truly triaxial testing device. The testing device is such that the samples can be subjected to a general three-dimensional state of stress. The test data is used to determine the material constants associated with the proposed constitutive model. The model is then verified by back-predicting the stress-strain curves obtained from the laboratory. As a final step, the proposed constitutive model is implemented into a three-dimensional finite element procedure. A number of boundary value problems are analyzed using the proposed model. The results are compared with the observation. It is found that the proposed model can effectively characterize the nonlinear and inelastic response of frictional materials. Although the proposed model is investigated with respect to soils, it can also be applied for concrete, rocks, etc.

Classically, fluid dynamics have been dealt with analytically because of the lack of numerical resources (Yeung, 1982). With the development of computational ability, many formulations have been developed which typically use the traditional Navier-Stokes equations along with an Eulerian grid. Today, there exists the possibility of using a moving grid (Lagrangian) along with a meshless discretization. The first issue in meshless fluid dynamics is the equations of motion. There are currently two types of Lagrangian formulations. Spherical Particle Hydrodynamics (SPH) is a method which calculates all equations of motion explicitly. The Moving Particle Semi-implicit (MPS) method uses a mathematical foundation based on SPH. However, instead of calculating all laws of motion explicitly, a fractional time step is performed to calculate pressure. A proposed method, Lagrange Implicit Fraction Step (LIFS), has been created which improves the mathematical formulations on the fluid domain. The LIFS method returns to Continuum mechanics to construct the laws of motion based on decomposing all forces of a volume. It is assumed that all forces on this volume can be linearly superposed to calculate the accelerations of each mass. The LIFS method calculates pressure from a boundary value problem with the inclusion of proper flux boundary conditions. The second issue in meshless Lagrangian dynamics is the calculation of derivatives across a domain. The Monte Carlo Integration (MCI) method uses weighted averages to calculate operators. However, the MCI method can be very inaccurate, and is not suitable for sparse grids. The Radial Basis Function (RBF) method is introduced and studied as a possibility to calculate meshless operators. The RBF method involves a solution of a system of equations to calculate interpolants. Machine expenses are shown to limit the viability of the RBF method for large domains. A new method of calculation has been created called Multi-dimensional Lagrange Interpolating Polynomials (MLIP). While Lagrange Interpolating Polynomials are essentially a one-dimensional interpolation, the use of "dimensional-cuts" and Gaussian quadratures can provide multi-dimensional interpolation. This paper is divided into three sections. The first section specifies the equations of motion. The second section provides the mathematical basis for meshless calculations. The third section evaluates the effectiveness of the meshless calculations and compares two fluiddynamic codes. / Fund number: N62271-97-G-0041. / US Navy (USN) author.

Geotechnical engineers are commonly faced with the need to perform ground improvement techniques to achieve the necessary bearing capacity for a project. Some of the most common techniques involve the excavation and replenishment of problematic geomaterial with one of better quality. Common projects, such as road embankments and retaining walls, also require the selection of backfill material. The guidelines for selecting backfill material are typically limited to complying with certain gradation bands, relative densities and allowable fines content. Round-grained silica sand, and beach sand from Boca Raton, FL, were used to generate a total of 16 binary granular mixtures containing different amounts of finer material, for which a series of direct shear tests were conducted. Based on the experimental results, it may be possible to provide an alternative criteria for selecting backfill material based on granulometric parameters and the amount of finer material. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

In this thesis, a 2D CHebyshev spectral domain decomposition method is developed for simulating the generation and propagation of internal waves over a topography. While the problem of stratified flow over topography is by no means a new one, many aspects of internal wave generation and breaking are still poorly understood. This thesis aims to reproduce certain observed features of internal waves by using a Chebyshev collation method in both spatial directions. The numerical model solves the inviscid, incomprehensible, fully non-linear, non-hydrostatic Boussinesq equations in the vorticity-streamfunction formulation. A number of important features of internal waves over topography are captured with the present model, including the onset of wave-breaking at sub-critical Froude numbers, up to the point of overturning of the pycnoclines. Density contours and wave spectra are presented for different combinations of Froude numbers, stratifications and topographic slope. / by Arjun Jagannathan. / Thesis (M.S.C.S.)--Florida Atlantic University, 2012. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

Cette thèse présente un cadre général pour l’étude de schémas de discrétisation nodaux sans maillageformulé en termes d’opérateurs discrets définis sur un nuage de points : intégration volumique et de bord, gradientet opérateur de reconstruction. Ces définitions dotent le nuage de points d’une structure plus faible que celledéfinie par un maillage, mais partageant avec elle certain concepts fondamentaux. Le plus important d’entre euxest la condition de compatibilité intégro-différentielle. Avec la consistance linéaire du gradient discret, cet analoguediscret de la formule de Stokes constitue une condition nécessaire à la consistance linéaire des opérateurs elliptiquesen formulation faible. Sa vérification, au moins de manière approchée, permet d’écrire des discrétisations dont le tauxde convergence est optimal. La construction d’opérateurs discrets compatibles est si difficile que nous conjecturons– sans parvenir à le démontrer – qu’elle nécessite soit la résolution d’un système linéaire global, soit la constructiond’un maillage : c’est "la malédiction sans-maillage". Trois grandes approches pour la construction d’opérateursdiscrets compatibles sont étudiées. Premièrement, nous proposons une méthode de correction permettant de calculerl’opérateur gradient compatible le plus proche – au sens des moindres carrés – sans mettre à mal la consistancelinéaire. Dans le cas particulier des gradients DMLS, nous montrons que le gradient corrigé est en réalité globalementoptimal. Deuxièmement, nous adaptons l’approche SFEM au cadre opérateur et constatons qu’elle définit desopérateurs consistants à l’ordre un et compatibles. Nous proposons une méthode d’intégration discrète exploitantla relation topologique entre les cellules et les faces d’un maillage qui préserve ces caractéristiques. Troisièmement,nous montrons qu’il est possible de générer tous les opérateurs sans maillage rien qu’avec la donnée d’une formuled’intégration volumique nodale en exploitant la dépendance fonctionnelle des poids volumiques nodaux par rapportà la position des noeuds du nuage, l’espace continu sous-jacent et le nombre de noeuds. Les notions de consistance desdifférents opérateurs sont caractérisées en termes des poids volumiques initiaux, formant un jeu de recommandationpour la mise au point de bonnes formules d’intégration. Dans ce cadre, nous réinterprétons les méthodes classiquesde stabilisation de la communauté SPH comme cherchant à annuler l’erreur sur la formule de Stokes discrète.L’exemple des opérateurs SFEM trouve un équivalent en formulation volume, ainsi que la méthode d’intégrationdiscrète s’appuyant sur un maillage. Son écriture nécessite toutefois une description très précise de la géométriedes cellules du maillage, en particulier dans le cas où les faces ne sont pas planes. Nous menons donc à bienune caractérisation complète de la forme de telles cellules uniquement en fonction de la position des noeuds dumaillage et des relations topologiques entre les cellules, permettant une définition sans ambigüité de leur volume etcentre de gravité. Enfin, nous décrivons des schémas de discrétisation d’équations elliptiques utilisant les opérateurssans-maillage et proposons plusieurs possibilités pour traiter les conditions au bord tout en imposant le moinsde contraintes sur la position des noeuds du nuage de points. Nous donnons des résultats numériques confirmantl’importance capitale de vérifier les conditions de compatibilité, au moins de manière approchée. Cette simple recommandation permet dans tous les cas d’obtenir des discrétisations dont le taux de convergence est optimal. / This thesis introduces a general framework for the study of nodal meshless discretization schemes. Itsfundamental objects are the discrete operators defined on a point cloud : volume and boundary integration, discretegradient and reconstruction operator. These definitions endow the point cloud with a weaker structure than thatdefined by a mesh, but share several fundamental concepts with it, the most important of them being integrationdifferentiationcompatibility. Along with linear consistency of the discrete gradient, this discrete analogue of Stokes’sformula is a necessary condition to the linear consistency of weakly discretized elliptic operators. Its satisfaction, atleast in an approximate fashion, yields optimally convergent discretizations. However, building compatible discreteoperators is so difficult that we conjecture – without managing to prove it – that it either requires to solve a globallinear system, or to build a mesh. We dub this conjecture the "meshless curse". Three main approaches for theconstruction of discrete meshless operators are studied. Firstly, we propose a correction method seeking the closestcompatible gradient – in the least squares sense – that does not hurt linear consistency. In the special case ofMLS gradients, we show that the corrected gradient is globally optimal. Secondly, we adapt the SFEM approachto our meshless framework and notice that it defines first order consistent compatible operators. We propose adiscrete integration method exploiting the topological relation between cells and faces of a mesh preserving thesecharacteristics. Thirdly, we show that it is possible to generate each of the meshless operators from a nodal discretevolume integration formula. This is made possible with the exploitation of the functional dependency of nodal volumeweights with respect to node positions, the continuous underlying space and the total number of nodes. Consistencyof the operators is characterized in terms of the initial volume weights, effectively constituting guidelines for thedesign of proper integration formulae. In this framework, we re-interpret the classical stabilization methods of theSPH community as actually seeking to cancel the error on the discrete version of Stokes’s formula. The example ofSFEM operators has a volume-based equivalent, and so does its discrete mesh-based integration. Actually computingit requires a very precise description of the geometry of cells of the mesh, in particular in the case where its facesare not planar. We thus fully characterize the shape of such cells, only as a function of nodes of the mesh andtopological relations between cells, allowing unambiguous definition of their volumes and centroids. Finally, wedescribe meshless discretization schemes of elliptic partial differential equations. We propose several alternatives forthe treatment of boundary conditions with the concern of imposing as few constraints on nodes of the point cloudas possible. We give numerical results confirming the crucial importance of verifying the compatibility conditions,at least in an approximate fashion. This simple guideline systematically allows the recovery of optimal convergencerates of the studied discretizations.