[pt] Expansão de tecido é um processo fisiológico, definido como a capacidade de uma membrana biológica aumentar em área superficial devido a uma deformação imposta. É um processo que pode ser induzido artificialmente, através de técnicas ligadas à cirurgia plástica reparadora que têm como objetivo expandir a pele para a sua utilização em áreas danificadas (queimaduras, grandes cicatrizese tatuagens), reconstrução mamária (após mastectomia), entre outras. Para expandir-se a pele artificialmente, implanta-se o expansor sob a camada da pele do paciente, numa região adjacente ao local onde se deseja efetuar a reconstrução. Em seguida, através de um tubo externo, introduz-se um fluido que irá provocar o aumento do volume inicial e, consequentemente, o aumento da área superficial da pele sobre o expansor. Este é um processo lento, feito em etapas, até que se obtenha a área superficial de pele desejada para cada fim. O objetivo desta dissertação é modelar matematicamente o fenômeno da expansão axissimétrica de tecido biológico, através da teoria da viscoelasticidade para grandes deformações. / [en] Tissue expansion is a well-known plastic surgery technique, based on the ability of biologic membranes to increase its surface area when a deformation is imposed. It is used to repair a wound area (scars, burns), to remove tattoos, in breast reconstruction, etc. This involves inserting a silicon-rubber prosthesis (expander) in its collapsed state under the subcutaneous tissue of the patient, closing the incision, and then inflating the expander slowly with a saline fluid through a one way valve. The skin expands in the form of a dome in unison with the balloon underneath it. The purpose of this work is modelling mathematically axially symmetric tissue expansion of biologic tissue, using Theory of Viscoelasticity for Finite Deformations. / [es] La expansión de tejidos es un proceso fisiológico, definido como la capacidad de una membrana biológica de aumentar su área superficial como consequencia de una deformación impuesta. Este proceso, que puede ser inducido artificialmente a través de técnicas de cirurgía plástica reparadora, tiene como objetivo expandir la piel para utilizarla en áreas dañadas (ejemplo: quemaduras o grandes cicatrices), reconstrucción mamaria (después de mastectomía, etc.) Para expandir la piel artificialmente, se implanta el expansor sobre la piel del paciente, en una región adyacente al local donde se desea efectuar la reconstrucción. Enseguida se introduce, a través de un tubo externo, un fluído que provocará el aumento del volumen inicial y, consequentemente, el aumento del área superficial de la piel sobre el expansor. Éste es un proceso lento, que se realiza por etapas hasta obtener la expansión del área superficial deseada, según los fines. El objetivo de esta disertación es modelar matemáticamente el fenómeno de la expansión asimétrica de tejido biológico, a través de la teoría de la viscoelasticidad para grandes deformaciones.

Dans les propulseurs de fusée, des instabilités aéroacoustiques et des interactions de type fluide-structure sont à l'origine de fortes oscillations de poussées pouvant déranger la poussée du moteur mais également causer des dommages non négligeables. On trouve dans les moteurs de fusée des protections thermiques de face (PTF) coincées entre les pains de propergol. Leurs déplacements se trouvent être la principale cause des interactions fluide structure (IFS) présentes dans les booster. Dans ce contexte, nous avons développé une approche numérique visant à simuler les problèmes d'IFS. Notre méthode se base sur le couplage de deux codes dissociés : l'écoulement est simulé avec CARBUR tandis que la dynamique des structures déformables est traitée par MARCUS. Une loi de comportement hyperélastique a été implémentée dans CARBUR afin de simuler le mouvement des PTF. Une campagne expérimentale a été menée dans notre laboratoire sur le tube à chocs T80 et en guide de validation du couplage des codes, les résultats numériques et expérimentaux ont été confrontés. / In a solid rocket motor, high pressure oscillations induced by aeroacoustic instabilities and fluid structure interaction (FSI) may lead to disturb rocket thrust and cause damages. In the rocket motors, flexible inhibitors made of insulating material are initially bonded to the propellant, and FSI is mainly induced by their displacement. In this context, a numérical approach to simulate FSI problems has been developped. Our method is based on the coupling of two dissociated codes : fluid flow is computed with CARBUR, while the dynamics of deformable structures is simulated by MARCUS. A hyperelastic behaviour law has been implemented in MARCUS in order to simulate the movement of flexible inhibitors. An experimental approach has been leaded in the shock waves tubes (T80) in our laboratory and as a validation of FSI coupling codes, numerical and experimental results have been compared.

[pt] O estudo do comportamento de membranas quando expostas a pressões e tensões de diverssos tipos, assim como de suas propriedades mecânicas nos últimos anos vem recebendo uma notável atenção em razão da variada aplicabilidade das membranas nas mais diversas áreas da engenharia, incluindo atuadores, robótica, sensores, aeroespacial, bioengenharia e estruturas infláveis para engenharia civil. Neste trabalho será apresentado um estudo numérico e experimental de uma membrana sujeita a uma endentação e perfuração transversalmente ao seu plano indeformado, considerando-se a presença do atrito na interface membrana-endentor, fato que torna esse estudo pioneiro nesta análise. Os estudos numéricos foram feitos no software Abaqus CAE. Os ensaios experimentais têm por objetivo comprovar os resultados numéricos e assim validá-los. Foram desenvolvidos aparatos experimentais dedicados aos ensaios pretendidos devido à ausência de equipamentos no mercado que pudessem reproduzir tais ensaios. / [en] The study of membranes behavior when subjected to pressures and tensions from all kinds, as well as their mechanical properties, is receiving a noticeable attention over the last years due to various applications of membranes on various engineering fields, including, actuators, robotics, sensors, airspace, bioengineering and inflatable structures for civil engineering. On this job will be presented a numerical and experimental study of a membrane subjected to an endentation and penetration transversally to the membrane’s undeformed plane, considering friction on the interface of the membrane and endentor, which makes this study a pioneer on this kind of analysis. The numerical studies were performed on Abaqus CAE finite element software. The experimental tests are intended to validate the numerical results. Experimental apparatus were developed especially to perform the tests done in this job.

The main focus of this work lies in the simulation of the deformation of mechanical components which consist of nonlinear elastic, incompressible material and that are subject to large deformations. Starting from a nonlinear formulation one can derive a discrete problem by using linearisation techniques and an adaptive mixed finite element method. This turns out to be a saddle point problem that can be solved via a Bramble-Pasciak conjugate gradient method. With some modifications the simulation can be improved.

[pt] Esta tese tem como objetivo analisar o comportamento estático não-linear e possíveis instabilidades de membranas e cascas hiperelásticas. Uma análise experimental detalhada de membranas e cascas com diferentes geometrias e submetidas à tração axial e pressão interna uniforme é realizada. Um aparato foi desenvolvido para possibilitar a tração da estrutura enquanto a mesma era preenchida por ar. As cascas e membranas utilizadas na análise experimental são compostas por elastômero isotrópico, homogêneo e hiperelástico, o qual é modelado como um material Neo- Hookeano incompressível, descrito por uma única constante elástica, ou por material do tipo Mooney-Rivlin ou Ogden, descritos por duas constantes elásticas. Estas constantes são obtidas pela comparação de resultados experimentais e numéricos para a estrutura sob tração axial uniforme. A estrutura foi discretizada utilizando-se elementos finitos de casca ou membrana mais apropriados e as equações de equilíbrio não-lineares resultantes resolvidas usando-se o programa de elementos finitos ABAQUS. Quando a estrutura tracionada é preenchida com ar observa-se que a pressão inicialmente cresce juntamente com o volume interno até um certo valor crítico. Após atingir este valor crítico um bulbo de deformação é formado subitamente num local ao longo do comprimento da estrutura e a pressão interna decresce subitamente, entretanto o volume interno da estrutura continua a crescer. Os resultados experimentais aproximam-se de maneira satisfatória aos resultados numéricos. Uma análise paramétrica detalhada é desenvolvida para estudar a influencia da tração inicial bem como dos parâmetros geométricos no comportamento não-linear e na capacidade de carga da estrutura. A influencia de diferentes tipos de imperfeições locais também é detalhadamente analisada. / [en] This thesis investigates the large deformations of hyperelastic membranes and shells. The static nonlinear behavior and possible instabilities of the membrane are both analyzed. A detailed experimental analysis was carried out involving cylindrical membranes and shells with different geometries and initial axial forces and the influence of the axial force and the internal pressure were investigated. An apparatus was developed to support vertically the extended structure while it is filled with air. The membranes and shells used in the experiments are composed of an isotropic, homogeneous and hyperelastic rubber, which is modeled as a Neo-Hookean incompressible material, described by a single elastic constant, or a Mooney-Rivlin or Ogden material, described by two elastic constants. Theses constants were obtained by comparing the experimental and numerical solutions for the structure under traction. The structure was discretized using appropriate membrane or shell finite elements and the resulting nonlinear equilibrium equations solved using the FE software ABAQUS. When the extended structure was filled with air, it was observed that the pressure increased initially as the volume increased until a certain critical value was reached, after which a bubble was suddenly formed along the structure and the internal pressure decreased markedly with increasing volume. The experimental results are, as shown in the thesis, in satisfactory agreement with the theory. A detailed parametric analysis was also carried out to study the influence of the initial traction and geometric parameters on the non-linear behavior and load carrying capacity of the structure. The influence of different types of local imperfections was also studied in detail.

Several geotechnical processes can only be reliably interpreted by taking account of the soil-atmosphere interactions. This thesis investigates two geotechnical problems involving soil-atmosphere interactions that drive water flow through the soil skeleton in two opposite directions; Problem 1: slope failure in expansive soils induced by water infiltration, Problem 2: large strain consolidation of soft soils induced by water evaporation. Both problems are of practical interest for safe and economical design of various geotechnical infrastructures. Two major geotechnical activities in the world; namely, the construction of water transfer canal in expansive soil area in China and the deposition of oil sands and hard rock tailings in Canada can be cited as classic examples of Problems 1 and 2, respectively. In such problems, substantial zones of the domain may switch between an unsaturated and saturated condition. Therefore, rational analysis requires simultaneous modelling of both unsaturated and saturated soil behaviour. The first goal of this thesis is to investigate the influence of swelling (the most characteristic behaviour of expansive soils) on slope stability using numerical methods. Swelling of expansive soils contributes to slope instability during rainfall because of two key reasons (i) soil swelling affects the flow process that actually induces swelling, (i.e. a typical coupling phenomenon), and (ii) swelling-induced stress redistribution and displacement development. In this thesis, the first effect is studied by a coupled (mechanical-hydraulic) numerical analysis of the response of a slope to rainfall using commercial software (GeoSlope). The second effect, the swelling-induced stress redistribution and displacement development after wetting, is tracked using a newly developed numerical program. In the program strain softening behaviour is introduced into the elasto-plastic Mohr-Coulomb Model for modelling unsaturated soil. A novel stress (net stress and suction)-dependent model for moduli of elasticity, combined with the predictive model for shear strength based on Soil Water Retention Behaviour are incorporated into the numerical program to achieve a smooth transition between saturated and unsaturated states. The results show that soil swelling can decrease the factor of safety by accelerating the wetting front depth due to hydro-mechanical coupling, while changes of sliding mass geometry has a negligible influence. The change of stress regime associated with soil swelling is significant to induce plastic strain softening (swelling-induced softening) and contribute to the slope failures. The second goal of thesis is to develop a novel computer program for simulation of large strain consolidation of soft soil under both self-weight and evaporation conditions. This program is both theoretically sound and practically applicable. Several basic/advanced constitutive models for unsaturated soils, including State Surface Model (SSM), Barcelona Basic model (BBM), Glasgow Coupled model (GCM) and bounding surface water retention model, are innovatively implemented into a piece-wise linear framework solved using finite difference technique. The developed program is referred to as UNSATCON-(ML), which has been tested using (a) existing analytical/numerical solutions and (b) various laboratory and field studies for single-layer and multiple-layer deposition of hard rock and oil sands tailings. Features of UNSATCON-(ML) that are improvements over existing models typically used to analyze consolidation-desiccation in soft soils include: (i) coupling of soil large deformation with true unsaturated water flow; (ii) correct reproduction of the shrinkage behaviour of soil under evaporation-induced desiccation; (iii) smooth transition between saturated and unsaturated states despite that some selected models are established using two independent stress variables, (iv) ensuring strictly mass conservation of water, and (v) simulation of irrecoverable volume change and hydraulic hysteresis to properly analyze multilayer tailings deposition. A number of hypothetical field case analyses are carried out using UNSATCON-ML, illustrating its applicability to industry.

[pt] Desenvolveu-se estudo teórico e numérico para simular o comportamento tensão-deformação de solos e rochas. Procurou-se estabelecer modelagem constitutiva apta a representar as peculiaridades inerentes ao comportamento destes materiais sob grandes deformações e degradação da estrutura. Dentro do contexto geotécnico brasileiro, o objetivo da pesquisa foi, também, investigar uma nova abordagem constitutiva para modelar o comportamento de solos moles, solos residuais e rochas sedimentares. O trabalho está dividido nos seguintes tópicos: revisão bibliográfica; estudo de medidas de deformações e taxas objetivas de tensões; definição e desenvolvimento dos modelos constitutivos a serem testados; definição dos algoritmos de retorno para integração das equações constitutivas; implementação em elementos finitos; simulação do comportamento observado em ensaios de laboratório. Os resultados da pesquisa indicam que o comportamento viscoso da argila mole do Sarapuí pode ser reproduzido corretamente adotando-se modelo constitutivo viscoplástico. A abordagem de solo estruturado está condizente com o comportamento do arenito de Vila Velha. Por fim, para modelar o comportamento de solos residuais dentro de um novo quadro constitutivo, foi proposta uma separação das deformações irreversíveis. / [en] A theoretical and numerical study was developed to simulate the stressstrain behavior of soils and rocks, formulating constitutive models able to catch the peculiarities inherent to the behavior of these materials under large strains and structure degradation. Within the Brazilian geotechnical context, the objective of the research was also to investigate constitutive approaches to model the behavior of soft soils, residual soils and sedimentary rocks. The work is divided into the following topics: literature review; study of strain measurements and objective stress rates; definition and development of the constitutive models to be tested; definition of the return mapping algorithms for integrating the constitutive equations; finite element implementation; and simulation of the behavior observed in laboratory tests. Results indicate that the viscous behavior of the Sarapuí soft clay can be correctly reproduced by adopting a viscoplastic constitutive model. The structured soil approach appears to be consistent with the behavior of Vila Velha sandstone. Finally, a decomposition of irreversible strains was proposed to model the behavior of residual soils within a novel constitutive framework.

No description available.

This thesis makes two noteworthy contributions in the are of mesh-free methods: a Pseudo-Divergence-Free (PDF) Element Free Galerkin (EFG) method which alleviates the volumetric locking and a Stabilized Updated Lagrangian formulation which allows to solve fast-transient dynamic problems involving large distortions. The thesis is organized in the following way. First of all, this thesis dedicates one chapter to the state of the art of mesh-free methods. The main reason is because there are many mesh-free methods that can be found in the literature which can be based on different ideas and with different properties. There is a real need of classifying, ordering and comparing these methods: in fact, the same or almost the same method can be found with different names in the literature. Secondly, a novel improved formulation of the (EFG) method is proposed in order to alleviate volumetric locking. It is based on a pseudo-divergence-free interpolation. Using the concept of diffuse derivatives an a convergence theorem of these derivatives to the ones of the exact solution, the new approximation proposed is obtained imposing a zero diffuse divergence. In this way is guaranteed that the method verifies asymptotically the incompressibility condition and in addition the imposition can be done a priori. This means that the main difference between standard EFG and the improved method is how is chosen the interpolation basis. Modal analysis and numerical results for two classical benchmark tests in solids corroborate that, as expected, diffuse derivatives converge to the derivatives of the exact solution when the discretization is refined (for a fixed dilation parameter) and, of course, that diffuse divergence converges to the exact divergence with the expected theoretical rate. For standard EFG the typical convergence rate is degrade as the incompressible limit is approached but with the improved method good results are obtained even for a nearly incompressible case and a moderately fine discretization. The improved method has also been used to solve the Stokes equations. In this case the LBB condition is not explicitly satisfied because the pseudo-divergence-free approximation is employed. Reasonable results are obtained in spite of the equal order interpolation for velocity and pressure. Finally, several techniques have been developed in the past to solve the well known tensile instability in the SPH (Smooth Particle Hydrodynamics) mesh-free method. It has been proved that a Lagrangian formulation removes completely the instability (but zero energy modes exist). In fact, Lagrangian SPH works even better than the Finite Element Method in problems involving distortions. Nevertheless, in problems with very large distortions a Lagrangian formulation will need of frequent updates of the reference configuration. When such updates are incorporated then zero energy modes are more likely to be activated. When few updates are carried out the error is small but when updates are performed frequently the solution is completely spoilt because of the zero energy modes. In this thesis an updated Lagrangian formulation is developed. It allows to carry out updates of the reference configuration without suffering the appearance of spurious modes. To update the Lagrangian formulation an incremental approach is used: an intermediate configuration will be the new reference configuration for the next time steps. It has been observed that this updated formulation suffers from similar numerical fracture to the Eulerian case. A modal analysis has proven that there exist zero energy modes. In the paper the updated Lagrangian method is exposed in detail, a stability analysis is performed and finally a stabilization technique is incorporated to preclude spurious modes.

Nous présentons deux approches différentes pour décrire le couplage hydromécanique des géomatériaux. Dans une approche de type phénoménologique nous traitons le milieu poreux comme un milieu continu équivalent dont les interactions entre la phase fluide et le squelette solide constituent le couplage du mélange à l'échelle macroscopique. En caractérisant le comportement de chaque phase nous arrivons à décrire le comportement couplé du milieu couplé saturé.Nous utilisons cette approche pour modéliser des essais expérimentaux faits sur un cylindre creux pour une roche argileuse (argile de Boom). Les résultats expérimentaux montrent de façon claire que le comportement de cette roche est fortement anisotrope. Nous avons choisi de modéliser ces essais en utilisant une lois de comportement élasto-plastique pour laquelle la partie élastique est transversalement isotrope.Le problème aux conditions aux limites étudié met en évidence des déformations localisées autour du forage intérieur. Afin de décrire de façon objective le développement de ces bandes de cisaillement nous avons considéré un milieu continu local de type second gradient qui permet d'introduire une longueur interne. De ce fait nous avons pu étudier le problème d'unicité en montrant qu'un changement de la discrétisation temporelle du problème aux limites peut conduire à des solutions différentes.Dans la deuxième approche étudiée nous caractérisons la microstructure du matériau avec des grains et un réseau de canaux pour la phase fluide. À l'aide d'un processus numérique d'homogénéisation nous arrivons à calculer numériquement la contrainte du mélange et le flux massique. Cette méthode d'homogénéisation numérique a été implémentée dans un code aux éléments finis afin d'obtenir des résultats macro. Une validation de l'implentation est proposée pour des calculs en mecanique pure et en hydromécanique. / We present two different approaches to describe the hydromechanical behaviour of geomaterials. In the first approach the porous media is studied through an equivalent continuum media where the interaction between the fluide and solid phases caracterize the coupling behaviour at the macroscale.We take into account this approach to model experimental tests performed over a hollow cylinder sample of clay rock (Boom Clay), considered for nuclear waste storage. The experimental results clearly show that the mechanical behaviour of the material is strongly anisotropic. For this reason we chose an elasto-plastic model based on Drucker-Prager criterion where the elastic part is characterized by cross anisotropy.The numerical results of boundary value problem clearly show localised strains around the inner hollow section. In order to regularize the numerical problem we consider a second gradient local continuum media with an enriched kinematic where an internal lenght can be introduced making the results mesh independent. The uniqueness study is carried out showing that changing the temporal discretization of the problem leads to different solutions.In the second approach we study the hydromechanical behaviour of a porous media that it is characterised by the microstructure of the material. The microstructure taken into account is composed by elastic grains, cohesives interfaces and a network of fluid channels. Using a periodic media a numerical homogenization (square finite element method) is considered to compute mass flux, stress and density of the mixture. In this way a pure numerical constitutive law is built from the microstructure of the media. This method has been implemented into a finite element code (Lagamine, Université de Liège) to obtain results at the macroscale. A validation of this implementation is performed for a pure mechanical boundary value problem and for a hydromechanical one.