O fenômeno de injeção de vapor em tanques de alívio é de relevância no projeto de reatores de água leve, sejam eles do tipo reator de água pressurizada (PWR) ou reator de água fervente (BWR). Este fenômeno permite a rápida absorção do vapor injetado em massa de água, por meio de sua condensação, uma vez que este vapor pode conter contaminantes químicos ou radiológicos que não permitem o seu descarte diretamente no ambiente. Desta forma, facilita-se a coleta do vapor produzido por descarga de vapor da água do resfriamento do reator, radiologicamente contaminada, e evita-se o que projeto de dispositivos e equipamentos necessite considerar a elevada pressão do vapor. A rapidez com que se dá a condensação é fruto de processos físicos que ocorrem na interface de vapor e água e que ainda não possuem modelo analítico e numérico definido. Em 1972 um modelo semi-empírico foi proposto, o qual, desde então, vem evoluindo. Não obstante, até o presente momento, não há modelo definitivo que se proponha a abranger toda extensão das condições experimentais. Estes modelos são fortemente dependentes do fluxo de massa que atravessa a interface de vapor e água, entretanto, até a presente data, não há expressão que determine este fluxo de massa, de tal forma que o valor de 275 Kg/m2/s vem sendo assumido como \"representativo da ordem de grandeza do fenômeno\" até o presente momento. Neste trabalho, é proposto um método de cálculo analítico do fluxo de massa, considerando-se como premissa a isentropia da injeção, e o desenvolvimento da 1ª e 2ª leis da Termodinâmica. Ainda, o fenômeno é analisado experimentalmente, por meio da análise dos dados produzidos no experimento do Circuito Termo Hidráulico de 150 bar (Loop 150), realizado nas dependências do CENTRO TECNOLÓGICO DA MARINHA EM SÃO PAULO. Por fim, um modelo numérico em software comercial foi desenvolvido para complementar a análise. Os resultados obtidos comprovam que a formulação isentrópica do fluxo de massa corrige de maneira satisfatória o fluxo de massa constante utilizado até então nos modelos semi-empíricos. Tal comprovação se deu através de análise numérica e da confrontação com dados experimentais obtidos na literatura. / The phenomenon of vapor injection in relief tanks presents relevance in the design of light water reactors, be they of the type pressurized water reactor (PWR) or boiling water reactor (BWR). This phenomenon allows the rapid absorption of the vapor injected in a mass of water, by condensation. Since this vapor may contain chemical or radiological contaminants that do not allow its discharge directly in the environment, it must be collected. The condensation avoids the design of devices and equipment, which need to consider the high vapor pressure, and allows the vapor to be collected. The rapidity with which the condensation occurs is the result of physical processes that occur at the interface of steam and water. These processes do not yet have a defined numerical and analytical model. In 1972 a semi-empirical model was proposed, which has, since then, evolved. Nevertheless, up to the present moment, there is no definitive model that intends to cover every extension of the experimental conditions. These models are strongly dependent on the mass flow through the steam and water interface, however, up to date, there is no expression that determines this mass flow. For the sake of this, the value of 275 kg / m2 / s has been assumed as \"representative of the order of magnitude of the phenomenon\" up to the present moment. In this work, a method of analytical calculation of mass flow is proposed, considering as premise the isotropy of the injection, and the development of the 1st and 2nd laws of thermodynamics. Still, the phenomenon is analyzed experimentally, by means of the analysis of the data produced in the experiment of Loop 150, realized in dependencies of the CENTRO TECNOLÓGICO DA MARINHA EM SÃO PAULO. Finally, a numerical model in commercial software was developed to complement the analysis. The result is proven with an isentropic mass flow formulation, which satisfactorily corrected the mass used in the former semi-empirical models. Such verification was performed through a series of data and confrontation with experimental data in the literature.

De maneira geral, o mercado náutico brasileiro ainda é muito restrito, principalmente o de pequenas embarcações. Nos últimos anos, porém, devido a uma maior exposição na mídia dos bons resultados internacionais de velejadores e exploradores brasileiros, a vela tem se popularizado. Esta dissertação descreve o projeto de um veleiro de pequeno porte para esporte/lazer fabricado em polietileno linear de média densidade (PEMD) pelo método da rotomoldagem. Este método tem se difundido rapidamente no exterior para a fabricação de equipamentos náuticos de pequeno porte, como veleiros e caiaques, proporcionando redução de custos e vantagens ambientais relacionadas ao processo de construção. A embarcação projetada é voltada para uma tripulação de duas pessoas adultas (ou um adulto e duas crianças) e foi dimensionada para um fácil transporte, possibilitando carregá-la sobre o bagageiro de um automóvel. O foco deste trabalho está no projeto naval. Desta forma, foram percorridas todas as etapas pertinentes de um projeto de veleiro, desde o projeto do casco, passando pelo projeto do plano vélico, projeto dos apêndices (bolina e leme), análise estrutural do casco em elementos finitos e verificação de desempenho comparativo com um veleiro bem conhecido no ramo da vela. Destaca-se o projeto do plano vélico, no qual, de forma otimizada, se obteve um conjunto de velas (mestra e buja) de bom desempenho, sem, contudo, comprometer a estabilidade do veleiro. Uma análise econômica preliminar indicou a possibilidade de se fabricar o veleiro rotomoldado com custo reduzido, abaixo do preço de mercado de veleiros do mesmo porte disponíveis no mercado nacional. Complementarmente, verificou-se também a possibilidade de se utilizar material reciclado na construção da embarcação, o que, além de ser uma alternativa para diminuir custos, proporciona benefícios ambientais ao minimizar sobras de produção. / In a general way, the Brazilian nautical market is still very restricted, specially the one of small dinghies. In the last years, however, mainly due to a greater exposure on the media based on good international results of Brazilian sailors and explorers, sailing has being popularized. This Msc. Thesis describes the design of a small sail dinghy, for sport or leisure use, made with medium density linear polyethylene using the method of rotomolding. This method has been spreading rapidly worldwide as a process of fabrication of small nautical crafts like sailboats and kayaks, since it results in cost reductions and environmental gains related to the construction process. The designed sailboat is directed for a crew of two adults (or an adult and two children), and was dimensioned for an easy transport, even on the top of a car. This work is focused on the development of the naval design. Therefore, it goes through all the design steps of a sailboat, starting with the design of the hull, and then going through the design of the sails, appendices (rudder and dagger board), hull structural analysis by Finite Elements Method (FEM) and verification of performance of the sailboat in comparison with a well known sailing dinghy. It should be highlighted, also, the sails designing process, which, in an optimized way, generated a set of sails (main and jib) of good performance, without, however, jeopardizing the stability of the sailboat. Through a preliminary economical analysis, it was verified that it is possible to produce a rotomolded sailboat with reduced cost, even below the market prices of national sailboats of this size. As a complement, the possibility of employing recycled material in the construction of the boat has been studied. Besides being an alternative to diminish costs, it can bring environmental benefits, as it minimizes production scraps.

Die geordneten mesoporösen Silikamaterialien SBA-15 und MCM-41 zeichnen sich durch lange zylindrische Poren aus, die auf einem 2D-hexagonalen Gitter arrangiert sind. Auf Grund dieser Eigenschaften finden sie vielfach Anwendung in der Industrie, bieten jedoch auch die Möglichkeit Sorptionsvorgänge und die dadurch induzierten Verformungen auf der Nanometerebene zu untersuchen. Dazu werden im ersten Teil dieser Arbeit Kleinwinkelröntgenstreuungsdaten mit Hilfe eines Formfaktormodells angefittet, um die Adsorption von Fluid in den Poren in Abhängigkeit vom Dampfdruck nachvollziehen zu können. Basierend auf diesen Ergebnissen wird ein Gittermodell eingeführt, welches die Vorgänge während der Sorption mit Hilfe heuristischer Füllmechanismen reproduziert und im Abgleich mit experimentellen Daten Auskunft über die Verteilung der Porosität auf Mikro- und Mesoporen in SBA-15 gibt. Weiterhin wird der Einfluss der begrenzten Geometrie auf die Selbstassemblierung von Tensiden in SBA-15 untersucht. Hierzu werden Neutronenstreudaten durch die Kombination eines Formfaktormodells für die Bragg-Streuung und des Teubner-Strey-Modells für die diffuse Streuung modelliert und interpretiert. Der zweite Teil der Arbeit beschäftigt sich mit den elastischen Verformungen der mesoporösen Materialien durch die Fluidsorption. Dazu wird eine Molekulardynamik-Simulation eines Lennard-Jones-Fluids in einer Schlitzpore vorgestellt, um den Ursprung dieser Verformungen auf der mikroskopischen Ebene zu untersuchen. Diese Ergebnisse fließen anschließend in ein makroskopisches Modell eines ganzen Kristalliten des mesoporösen Materials ein, wodurch ein einfaches Multiskalenmodell entsteht. Die makroskopische Ebene wird dabei durch eine Finite-Elemente-Simulation beschrieben, die im Abgleich mit experimentellen Daten weitere Aussagen über die elastischen Eigenschaften des Materials erlaubt. / The ordered mesoporous silica materials SBA-15 and MCM-41 consist of long cylindrical pores arranged on a 2D-hexagonal lattice. Due to these features, they are used for a range of industrial applications but provide also a possibility to study sorption processes and sorption-induced deformations on the nanoscale. In the first part of this work small-angle X-ray scattering data are fitted with a form factor model in order to examine fluid adsorption in the pores. Based on these results a lattice model is introduced which reproduces the sorption process using heuristic filling mechanisms and clarifies how the porosity of SBA-15 is composed out of micro- and mesopores. Furthermore, the influence of the confined geometry on the self-assembly of surfactants in SBA-15 is studied. For this, neutron scattering data are modeled and interpreted by the combination of a form factor model for the Bragg scattering and the Teubner-Strey model for the diffuse scattering. The second part of this work focuses on the elastic deformations caused by fluid sorption in the mesoporous materials. A Molecular Dynamics simulation of a Lennard-Jones fluid in a slit-pore is presented in order to reveal the origin of these deformations on the microscopic scale. These results are subsequently implemented into a macroscopic model of whole crystallite, thereby creating a simple multi-scale model. The macroscopic scale is modeled with a Finite Elements simulation, which by comparison with experimental data delivers further insights into the elastic properties of the material.

Das Thema dieser Dissertation ist die Herleitung und numerische Analyse von finiten Elementen für ein Problem in der Elastoplastizität mit Kontaktbedingungen. Die hergeleiteten finite Elemente Verfahren basieren auf einer Formulierung als Sattelpunktproblem und der Nutzung von Polynomen höherer Ordnung. Die Analyse der vorgestellten Verfahren beginnt mit dem Zeigen der Wohldefiniertheit und der Konvergenz. Im nächsten Schritt werden a priori Abschätzungen der Konvergenzraten gezeigt. Weiterhin führt die Einführung von Lagrange Multiplikatoren zu einem einheitlichen Ansatz zur a posteriori Abschätzung des Diskretisierungfehlers unter der Verwendung von Elementen höherer Ordnung. Zusätzlich ermöglicht es der Zugang über Lagrange Multiplikatoren die Äquivalenz der Diskretisierungsfehler in den Spannungen und in den Energien für finite Elemente niederer Ordnung zu zeigen, was insbesondere neu für Viereckselemente ist. Diese Äquivalenz wiederum erlaubt nun den Beweis der Konvergenz von adaptiven finiten Elementen niederer Ordnung. Für Dreieckselemente wird sogar die optimale Konvergenz bewiesen. Die theoretischen Erkenntnisse werden durch numerische Experimente bestätigt. / The topic of this thesis is the derivation and analysis of some finite element schemes for a contact problem in elastoplasticity. These schemes are based on the formulation of the models as saddle point problems and use finite element spaces of arbitrary polynomial degrees. In this thesis, these new approaches with higher-order finite elements are shown to be well defined and convergent. Moreover, some a~priori estimates on the rates of convergences are proven. The use of Lagrange multipliers in the saddle point formulation yields a coherent approach to reliable a~posteriori error estimates for the proposed higher-order schemes. Additionally, the Lagrange multipliers are used to show the equivalence of the errors of the stresses and the energies, for low order finite elements using triangular or quadrilateral cells. For the first time, this allows for a proof of convergence for quadrilateral-based adaptive finite elements. Furthermore, the approach based on triangular cells is shown to be of optimal convergence. The theoretical findings are confirmed by numerical experiments.

Les bases de fonctions sont des outils indispensables de la géométrie numérique puisqu'ils permettent de représenter des fonctions comme des vecteurs, c'est à dire d'appliquer les outils de l'algèbre linéaire à l'analyse fonctionnelle. Dans cette thèse, nous présentons plusieurs constructions de bases de fonctions sur des surfaces pour la géométrie numérique. Nous commençons par présenter les bases de fonctions usuelles des éléments finis et du calcul extérieur discret, leur théorie et leurs limites. Nous étudions ensuite le Laplacien et sa discrétisation, ce qui nous permettra de construire une base de fonctions particulière~: les fonctions propres de l'opérateur de Laplace-Beltrami, ou harmoniques variétés. Celles-ci permettent de généraliser la transformée de Fourier et le filtrage spectral aux fonctions définies sur des surfaces. Nous présentons ensuite des applications de cette base de fonction à la géométrie numérique. En particulier, nous montrons qu'une fois calculée, cette base de fonction permet de filtrer la géométrie en temps interactif. Pour pouvoir définir des bases de fonctions de façon plus indépendante du maillage de la surface, nous nous intéressons ensuite aux paramétrisations globales, et en particulier aux champs de directions à symétries qui permettent de les définir. Ainsi, dans la dernière partie, nous étudions ces champs de directions à symétries, et en particulier leur géométrie et leur topologie. Nous donnons alors des outils pour les construire, les manipuler et les visualiser / Function bases are fundamental objects in geometry processing as they allow to represent functions as vectors, that is to apply tools from linear algebra to functional analysis. In this thesis, we present various constructions of useful functions bases for geometry processing. We start by presenting usual function bases, their theory and limits. We then study the Laplacian operator and its discretization, and use it to define a particular function basis: Laplacian eigenfunctions or Manifold harmonics. The Manifold Hamonics form a function basis that allows to generalize the Fourier transform and spectral filtering on a surface. We present some applications and extensions of this basis for geometry processing. To define function bases in a mesh-independant manner, we need to build a global parameterization, and especially the direction fields required to define them. Thus, in the last part of this thesis we study N-symmetry direction fields on surfaces, and in particular their geometry and topology. We then give tools to build, edit, control and visualize them

Les accouplements (ou coupleurs) magnétiques servent à transmettre le couple d'un moteur vers sa charge sans contact mécanique. La suppression de ces contacts permet de réduire les bruits et vibrations, d'augmenter la fiabilité et d'assurer l'étanchéité dans des environnements difficiles. Dans le cas des moteurs supraconducteurs, un accouplement utilisant des matériaux supraconducteurs permet une nette augmentation des performances tout en transmettant le couple entre un environnement cryogénique (cryostat) et la température ambiante. Ce mémoire porte sur l'étude de coupleurs magnétiques à base de supraconducteurs à haute température critique (HTC) et d'aimants permanents. Deux topologies sont proposées, l'une à flux radial et l'autre à flux axial. Des outils analytiques et numériques sont développés pour le dimensionnement des accouplements étudiés. Un modèle analytique 2D de calcul du champ magnétique dans un accouplement supraconducteur à flux radial est développé et validé par éléments finis. Ce modèle est par la suite utilisé dans une procédure d'optimisation par algorithmes génétiques. L'objectif étant de rechercher les dimensions de l'accouplement qui maximisent le couple et minimisent la longueur du fil supraconducteur. Un prototype d'accouplement à flux axial est aussi réalisé. Plusieurs essais de caractérisation des bobines HTC sont menés. Des résultats de mesure de champ magnétique, de courant critique et de couple sont présentés / Magnetic couplings (or couplers) are used to transmit torque from a prime mover to its load without mechanical contact. This contactless transmission allows to reduce noise and vibration, to increase reliability and ensure hermetic isolation in severe environments. When the prime mover is a superconducting motor, a coupler which uses superconducting materials has more torque transmission capabilities and enables to transmit torque between a cryogenic media (cryostat) and the ambient temperature. This work focuses on the study of magnetic couplers using high temperature superconductors (HTS) and permanent magnets. Radial and axial field magnetic couplings, for which we developed analytical and numerical design tools, are proposed. A 2D analytical model for calculating the magnetic field distribution in a flux focusing HTS coupling is developed and validated by finite element computations. This model is then embedded in a genetic algorithms optimization procedure. The aim is to find the dimensions of the coupling that maximize torque and minimize the overall length of the HTS wires. A prototype axial field HTS coupler has been also designed, constructed and tested. Several tests have been conducted to characterize the HTS coils. Results of magnetic field, critical current and torque measurements are presented

Dans cette thèse, nous proposons de nouvelles méthodes permettant de résoudre numériquement des problèmes de diffraction harmoniques et tridimensionnels, aussi bien acoustiques qu'électromagnétiques, pour lesquels l'objet diffractant est pénétrable et inhomogène. La résolution de tels problèmes est centrale pour des calculs de surfaces équivalentes sonar et radar (SES et SER). Elle est toutefois connue pour être difficile car elle requiert de discrétiser des équations aux dérivées partielles posées dans un domaine extérieur. Étant infini, ce domaine ne peut pas être maillé en vue d'une résolution par la méthode des éléments finis volumiques. Deux approches classiques permettent de contourner cette difficulté. La première consiste à tronquer le domaine extérieur et rend alors possible une résolution par la méthode des éléments finis volumiques. Étant donné qu'elles approximent les problèmes de diffraction au niveau continu, les méthodes de troncature de domaine peuvent toutefois manquer de précision pour des calculs de SES et de SER. Les problèmes de diffraction harmoniques, pénétrables et inhomogènes peuvent également être résolus en couplant une formulation variationnelle volumique associée à l'objet diffractant et des équations intégrales surfaciques rattachées au domaine extérieur. Nous parlons de couplages FEM-BEM (Finite Element Method-Boundary Element Method). L'intérêt de cette approche réside dans le fait qu'elle est exacte au niveau continu. Les couplages FEM-BEM classiques sont dits forts car ils couplent la formulation variationnelle volumique et les équations intégrales surfaciques au sein d'une même formulation. Ils ne sont toutefois pas adaptés à la résolution de problèmes à haute fréquence. Pour pallier cette limitation, d'autres couplages FEM-BEM, dits faibles, ont été proposés. Ils correspondent concrètement à des algorithmes de décomposition de domaine itérant entre l'objet diffractant et le domaine extérieur. Dans cette thèse, nous introduisons de nouveaux couplages faibles FEM-BEM acoustiques et électromagnétiques basés sur des approximations de Padé récemment développées pour les opérateurs Dirichlet-to-Neumann et Magnetic-to-Electric. Le nombre d'itérations nécessaires à la résolution de ces couplages ne dépend que faiblement de la fréquence et du raffinement du maillage. Les couplages faibles FEM-BEM que nous proposons sont donc adaptés pour des calculs précis de SES et de SER à haute fréquence / In this doctoral dissertation, we propose new methods for solving acoustic and electromagnetic three-dimensional harmonic scattering problems for which the scatterer is penetrable and inhomogeneous. The resolution of such problems is key in the computation of sonar and radar cross sections (SCS and RCS). However, this task is known to be difficult because it requires discretizing partial differential equations set in an exterior domain. Being unbounded, this domain cannot be meshed thus hindering a volume finite element resolution. There are two standard approaches to overcome this difficulty. The first one consists in truncating the exterior domain and renders possible a volume finite element resolution. Given that they approximate the scattering problems at the continuous level, truncation methods may however not be accurate enough for SCS and RCS computations. Inhomogeneous penetrable harmonic scattering problems can also be solved by coupling a volume variational formulation associated with the scatterer and surface integral equations related to the exterior domain. This approach is known as FEM-BEM coupling (Finite Element Method-Boundary Element Method). It is of great interest because it is exact at the continuous level. Classical FEM-BEM couplings are qualified as strong because they couple the volume variational formulation and the surface integral equations within one unique formulation. They are however not suited for solving high-frequency problems. To remedy this drawback, other FEM-BEM couplings, said to be weak, have been proposed. These couplings are actually domain decomposition algorithms iterating between the scatterer and the exterior domain. In this thesis, we introduce new acoustic and electromagnetic weak FEM-BEM couplings based on recently developed Padé approximations of Dirichlet-to-Neumann and Magnetic-to-Electric operators. The number of iterations required to solve these couplings is only slightly dependent on the frequency and the mesh refinement. The weak FEM-BEM couplings that we propose are therefore suited to accurate SCS and RCS computations at high frequencies

Dans cette thèse, nous étudions la formation de domaines ferroélectriques dans des nanostructures, à partir d'une modélisation faisant intervenir les équations de Ginzburg-Landau et d’Électrostatique, ainsi que des conditions aux limites d'application potentielle. Dans la première partie de la thèse, les nanostructures sont constituées d'une couche ferroélectrique entièrement enclavée dans un environnement paraélectrique. Nous introduisons un modèle depuis un couplage de ces équations et élaborons, pour son investigation, un schéma numérique faisant usage d’Éléments Finis. Des simulations numériques montrent l'efficacité de ce schéma, qui permet d'établir, par exemple, l'existence de cycles d'hystérésis sous l'influence de paramètres aussi bien physiques que géométriques. Dans la seconde partie, les nanostructures sont constituées d'une couche ferroélectrique partiellement enclavée qui s'intercale entre deux couches paraélectriques. Deux modèles sont proposés à partir d'une variante du couplage réalisé dans la première partie, et se distinguent dans la prescription des conditions aux limites. Des conditions de type Neumann interviennent dans le premier modèle, pour lequel un schéma numérique aussi basé sur des approximations par Eléments Finis est introduit. Dans le second modèle, des conditions périodiques sont prises en considération ; un schéma numérique s'appuyant ici sur une hybridation des méthodes de Différences Finies et d'Eléments Finis est présenté. Les simulations numériques basées sur ces deux schémas permettent de renseigner sur les permittivités dites effectives, des nanostructures, ou encore sur la constitution des parois de domaines ferroélectriques / In this thesis, we study the formation of ferroelectric domains in nanostructures by modeling based on the Ginzburg-Landau and Electrostatics equations, together with boundary conditions that are suitable for real applications. In the first part of the thesis, the nanostructures are made up of a ferroelectric layer, fully enclosed in a paraelectric environment. We introduce a model based on the coupled system of equations and then develop, for its investigation, a numerical scheme using Finite Elements. Numerical simulations show the efficiency of this scheme, which allows us to establish, for instance, the existence of hysteresis cycles under the influence of physical or geometric parameters. In the second part, the nanostructures are made up of a partially enclosed ferroelectric layer that lies between two paraelectric layers. Two models are introduced from a variant of the coupling performed in the first part, and differ in the prescription of the boundary conditions. Neumann type conditions are prescribed in the first model, for which a numerical scheme also based on Finite Element approximations is developed. In the second model, periodic conditions are taken into account; a numerical scheme based on a combination of Finite Difference and Finite Element methods is presented. Numerical simulations from these schemes allow us, for instance, to investigate the so-called effective permittivities, of the nanostructures, or the formation of ferroelectric domain walls

[pt] A modelagem de materiais biológicos para o entendimento de diversas práticas cirúrgicas na medicina, tem se mostrado a cada dia mais importante. Na cirurgia plástica, reparadora ou estética, o conhecimento do comportamento da pele humana, in vivo, é de fundamental importância nos processos cirúrgicos. Nos últimos anos, mais precisamente desde 1957, uma técnica realizada pela cirurgia plástica, conhecida como expansão de pele, vem sendo cada vez mais utilizada. Esta técnica tem como objetivo a obtenção de uma quantidade adicional de pele, para a utilização na recuperação de queimados, reconstrução mamária, retirada de pele com aparência indesejada e outras aplicações. Este trabalho tem como objetivo fornecer aos médicos o conhecimento do comportamento da pele, através de uma análise numérica e experimental, quando submetida ao processo de expansão. Durante o desenvolvimento deste trabalho, estaremos mostrando a metodologia adotada para estudar a pele humana e os resultados alcançados com o acompanhamento de pacientes submetidos a este tipo de processo cirúrgico. Para atingir o objetivo, foram estudadas diversas equações constitutivas, procurando as melhores constantes viscoelásticas, que descrevam o comportamento da pele sob expansão. No estudo realizado, avaliamos ainda as mudanças das constantes viscoelásticas durante a evolução da expansão e o comportamento da pele em diferentes regiões do corpo humano. Nos resultados apresentados, encontramos erros máximos para as constantes da equação constitutiva adotada, na ordem de 28 por cento. Estudos recentes envolvendo a pele humana apresentam erros na ordem de 75 por cento, para as constantes elásticas do material. Com a análise dos resultados, mostramos o comportamento da pele humana, em seres vivos, em diferentes regiões do corpo. O conhecimento de uma equação constitutiva, ou seja, da relação entre as tensões e deformações que ocorrem na pele durante o processo de expansão, proporcionará aos médicos a possibilidade de avaliar as diversas técnicas utilizadas na cirurgia plástica em geral : a expansão de pele, a reconstrução mamária, análise de suturas, análise de cicatrizes, comportamento da pele durante uma incisão, cirurgias estéticas da face (face lifting), e outras aplicações. / [en] The modeling of biological materials is really important today, for the agreement of diverse practical surgical in the medicine. In the area of plastic surgery, the knowledge of the behavior of the human skin has a basic importance in the surgical processes. Since 1957, one technique in plastic surgery, known as skin expansion, has been much used. This technique has as objective the attainment of an additional amount of skin, for the use in the burned patients, breast reconstruction, removal of skin with not desired appearance is and other applications. This work has as objective supply to doctors the knowledge of the skin behavior, through a numerical and experimental analysis, when submitted to the expansion process. During the development of this work, we will show the methodology used to study the human skin and the results reached with the accompaniment of patients submitted to this type of surgical process. To reach the objective, different constitutive equations had been studied, looking for the best viscoelastic constants, to describe the behavior of the skin under expansion. In the study, we also evaluate the changes of the constants during the evolution of the expansion and the behavior of the skin in different regions of the human body. In the presented results, we find maximum errors for the constants of the adopted constitutive equation, to be in 28 percent order. Recent studies involving the human skin present errors in the order of 75 percent, for the elastic constants of the material. With the analysis of the results, we will be show to the behavior of the human skin, in vivo, in different regions of the body. The knowledge of a constitutive equation, that is, of the behavior of the stresses and strains that occur in the skin during the expansion process, will provide to the doctors the possibility to evaluate the diverse techniques used in the plastic surgery: The expansion of skin, breast reconstruction, analysis of sutures, analysis of scars, behavior of the skin during an incision, face lifting, and other applications.

[pt] Este trabalho apresenta o desenvolvimento de um sistema integrado de modelagem, tridimensional, de fluxo e transporte em meios porosos e fraturados. O sistema é composto de seis programas computacionais, que são responsáveis pela geração de superfícies geológicas (Gocad), geração de sistemas de fraturas (FracGen3D), modelagem geométrica (MG), análise numérica de fluxo e transporte (soluto e partículas) (FTPF-3D) e visualização dos resultados (Pos3D e Matlab). Dos programas, dois foram desenvolvidos neste trabalho (FracGen3D e o FTPF-3D) e quatro foram integrados ao sistema (Gocad, MG, Pos3D e Matlab). O sistema é capaz de modelar os meios porosos, fraturados, porosos fraturados (meio poroso e fraturado interposto) e uma combinação entre os meios. Nos meios fraturados ou porosos fraturados, as fraturas geradas podem ser do tipo determinísticas e/ou estatísticas. As características das fraturas estatísticas podem ser geradas segundo distribuições probabilísticas ou com valores constantes. O programa de análise numérica utiliza o Método dos Elementos Finitos para resolver as equações governantes, considerando os regimes permanente e transiente, em condições saturadas e não saturadas. Para a solução da não linearidade da equação de fluxo, é adotado o método de Picard ou o método BFGS. No transporte de solutos, os mecanismos de advecção, dispersão, difusão, sorção e decaimento podem ser considerados. O trabalho apresenta exemplos numéricos utilizados na validação das implementações computacionais realizadas, e apresenta também, outros exemplos utilizados para demonstrar o sistema desenvolvido. / [en] This work presents the development of an integrated system for the threedimensional modelling of flow and transport in porous and fractured media. The system is composed of six computational programs, which are responsible for the generation of geologic surface (Gocad), generation of fracture network (FracGen3D), geometric modelling (MG), numerical analysis of flow and transport (solute and particles) (FTPF-3D) and results visualization (Pos3D and Matlab). Of the programs, two had been developed in this work (FracGen3D and the FTPF-3D) and four had been integrated to the system (Gocad, MG, Pos3D and Matlab). The system is able to model the porous, fractured, fractured porous media (porous and fractured medias interposed) and a combination between the media. In the fractured or fractured porous media, the fractures generated can be of the type deterministic and/or statistical. The characteristics of the statistical fractures can be generated according to probabilistic distributions or with constant values. The numerical analysis program uses the Finite Element Method to solve the governance equations, considering steady-state and transient flow, in saturated and unsaturated conditions. For the solution of non linearity of the flow equation, the Picard scheme or the BFGS scheme are adopted. In the solute transport, the advection, dispersion, diffusion, sorption and decay mechanisms can be considered. This work also presents numerical examples used in the validation of the carried through computational implementations and other examples used to demonstrate the system that has been developed.