Quando o concreto é submetido a ações especiais, como cargas cíclicas ou ação de cargas de impacto, modificações em sua composição são necessárias, já que o concreto não apresenta desempenho satisfatório à tração, o que compromete o seu comportamento frente à ação de cargas dinâmicas. Uma alternativa para amenizar esta deficiência consiste em adicionar fibras ao concreto. Estas atuam como reforços à tração, transformando a matriz cimentícia, tipicamente frágil, em um material que apresenta boa resistência residual após a fissuração. Buscando colaborar na avaliação da eficiência de diferentes tipos de fibras, o presente trabalho analisa o comportamento de concretos com fibras de aço, submetidos ao impacto, avaliando a influência do fator de forma, do comprimento e do teor de fibras, assim como do tamanho do agregado. São ainda analisados os efeitos da incorporação de fibras na resistência à compressão, na resistência à tração por compressão diametral, no módulo de elasticidade e na tenacidade dos compósitos. Adicionalmente, é executada uma comparação entre os resultados experimentais e os derivados de um esquema de modelagem da situação de impacto através do uso do método de elementos discretos. Buscou-se, através da modelagem teórica, executar um mapeamento dos danos, provocados por cargas de impacto incrementais, ao longo do tempo, bem como determinar as energias necessárias para levar as placas até a ruptura. Os resultados indicam que a incorporação de fibras de aço não consegue retardar o aparecimento da primeira fissura, mas aumenta significativamente a tenacidade dos compósitos. Fibras mais longas e com maior fator de forma tendem a ser mais eficientes, desde que se supere um teor de fibras mínimo, que neste trabalho ficou em torno de 100.000 fibras/m3, para fibras longas (50-60 mm) e de 400.000 fibras/m3, para fibras curtas, cuja ancoragem é menos eficiente. O método de teste de impacto por queda de esfera se mostrou adequado e sensível, porém o esquema de modelagem numérica testado necessita ser refinado para permitir uma adequada simulação do comportamento de concretos com fibras. / When submitted to special loading patterns, derived from dynamical actions such as cyclic or impact loads, concrete elements need to be reinforced, in order to resist the tensile stresses. A feasible alternative, in such cases, is to incorporate fibers in the concrete matrix. The fibers act as a tensile reinforcement, transforming the fragile cement matrix into a composite with significant post-cracking residual strength. In order to contribute with the data collection about the efficiency of different fiber types, the present research work presents an analysis of the behavior of steel fiber reinforced concretes subjected to impact loads. The work investigates the influences of changes in the shape factor, length and amount of fibers. The effects of these combinations on other basic properties of the composites, such as compression strength, split cylinder tensile strength, Young’s modulus and tenacity is also measured. Additionally, a comparison is made between the experimental results from the impact tests and the estimates obtained from a theoretical model that uses the discrete element method (DEM). This theoretical approach aimed to determine if the model was able to simulate the damage evolution over time generated by the increasing impacts loads, as well as to determine the total energy necessary to crack and break the specimens. The results obtained pointed out that the introduction of steel fibers does not affect the energy for the first crack but increases significantly the tenacity of the composite. Longer fibers, with greater shape factors, tend to be more efficient, provided that the fiber content is sufficiently high. The minimum recommended fiber content, according to the data from this research, may be around 100.000 fibers/m3, for longer fibers (50-60 mm). Or around 400.000 fibers/m3, for shorter fibers, which are not so efficient in terms of anchorage. The impact test method developed was considered adequate, being sensitive to the phenomenon and providing reliable data. The DEM model, however, needs to be refined to be able to deal with fiber concrete composites.

Quando o concreto é submetido a carregamentos especiais, como cargas cíclicas ou ação de cargas de impacto, modificações em sua composição são necessárias. Uma vez que o material não apresenta desempenho satisfatório à tração, seu comportamento frente a este tipo de carregamento acaba seriamente comprometido. Uma alternativa para amenizar esta deficiência consiste em adicionar fibras de aço ao concreto. Ao adicionar estes elementos à matriz cimentícia, promove-se meios de transferência de tensões através das fissuras, aumentando a tenacidade do material, proporcionando mecanismos de absorção, relacionados com o desligamento e o arrancamento de fibras. Um número significativo de trabalhos experimentais envolvendo os mais diversos tipos de elementos estruturais reforçados com fibras de aço está disponível, havendo, no entanto, uma forte carência sob o ponto de vista de simulações numéricas. Buscando colaborar no desenvolvimento do material, o presente trabalho propõe a aplicação do Método dos Elementos Discretos para simulação do compósito submetido a carregamentos estáticos e dinâmicos. São realizadas alterações no algoritmo do método a fim de realizar a dispersão de fibras de aço na matriz de concreto. A análise das condições de contorno utilizadas em trabalho anterior revela a necessidade de aplicação de apoios elásticos sob pena de superestimar a rigidez do modelo. Os diagramas carga versus deslocamento que resultaram dos ensaios estáticos demonstram que o modelo criado é sensível à adição de fibras: maiores teores conduzem a modelos com maior tenacidade. O ensaio de impacto também se mostrou sensível e o padrão de fissuração encontrado nas simulações revelou uma boa aproximação com ensaios experimentais anteriores. / When submitted to special loading patterns, derived from dynamical actions such as cyclic or impact loads, some alterations in the concrete constitution need to be done, since the material don’t have an adequate behavior under tensile stress. A feasible alternative, in such cases, is to incorporate steel fibers in the concrete matrix. Adding these elements, stress transference mechanisms along the cracks are promoted, increasing the material tenacity. An expressive number of experimental works involving all the kinds of steel fiber reinforced concrete structural elements are available. However, few researches based on numerical methods are found in the literature. In order to contribute with the data collection and the development of the material, the present research work proposes the application of the Discrete Element Method to simulate the composite subjected to static and dynamic loads. Some modifications are made on the method algorithm trying to create the dispersion of fibers in the concrete matrix. The analysis of the boundary conditions used on previous work reveal the importance of using elastic support to don’t overestimate the stiffness of the model. The diagram load versus displacement that came from the static simulations shows that the model is sensible to the addition of fibers: higher proportions of fiber leads to models with higher tenacity. The impact tests also demonstrate sensibility and the crack pattern found on the simulations presented a very good approximation to previous experimental work.

Ce travail de thèse concerne la prédiction des structures en béton soumises à des chargements extrêmes. Il s'intéresse plus particulièrement au comportement du béton sous fort confinement où la contrainte peut atteindre des niveaux de l'ordre du giga Pascal. La modélisation de ce comportement doit être capable de reproduire la compaction irréversible. Pour ce faire, deux lois de comportement élasto-plastique - endommageable ont été développées et implantées dans un code aux éléments discrets. Les paramètres utilisés dans ces lois sont calibrés par les simulations des essais de traction/compression uniaxial, des essais hydrostatiques et triaxiaux. Une fois les paramètres calibrés, la loi montrant le meilleur agrément avec l'expérience a été choisie pour la prédiction de la réponse du béton sous différents niveaux de confinement. Les résultats du modèle sont analysés non seulement à l'échelle macroscopique mais également à l'échelle de l'élément discret. La nécessité de prendre en compte une loi d'interaction de type élasto-plastique-endommageable est aussi montrée. La deuxième partie du travail de thèse développe une méthode de couplage entre le modèle éléments discrets et un modèle d'écoulement compressible en tenant compte des mécanismes physiques fondamentaux d'interaction entre l'écoulement interne et les particules solides d'un matériau poreux. Le problème d'écoulement est résolu par une méthode en volumes finis, où le volume est discrétisé en tétraèdres issus d'une triangulation régulière de Delaunay. Notre modèle est une adaptation aux fluides compressibles d'un modèle développé initialement pour les écoulements incompressibles. Ce couplage a été utilisé pour simuler le comportement triaxial des bétons humides et saturés sous différents niveaux de confinement. Les résultats nous montrent une bonne reproduction du comportement non-drainé du béton saturé sous faible confinement. Pour fort confinement, les simulations ne se rapprochent des résultats expérimentaux qu'au prix d'une compressibilité du fluide plus faible que celle de l'eau. Par ailleurs, la contrainte effective était une variable pertinente pour décrire le comportement du béton humide par un état limite intrinsèque indépendant du degré de saturation. / This thesis work deals with the predicting of concrete structures submitted to some extreme loadings, and, more particularly, focuses on behavior of concrete under a high-confining pressure. At this range of pressures, irreversible compaction of the material occurs and needs to be considered. Doing so, two elasto-plastic-damaged constitutive laws have been developed and implanted into a discrete element numerical code. Local parameters to be used in these constitutive laws are identified by simulating reference uniaxial traction/compression tests and triaxial compression tests. Once these parameters have been obtained, the law showing the best agreement with the experimental data has been chosen to predict the reponse of concrete sample for triaxial compressive tests at different levels of confinement. The numerical results have been analyzed not only at macroscopic scale but also at discrete element scale. The need of a constitutive law taking into account the elasto-plastic-damaged behavior has been also proved. The second objective of the thesis work was to develop a fluid flow – coupled discrete element model by considering fundamental physical mechanisms of the interaction between the internal fluide flow and the solid particles of a porous material. The flow problem is solved by the finite volume method, where the volume is discretized into tetrahedra issue of a regular Delaunay triangulation. Our model is an adaptation for elastic fluids of a model originally developed for incompressible flows. The developed fluid-flow coupled discrete element has been used to simulate the undrained triaxial behavior of concrete under different levels of confinement. The results show a good reproduction of undrained behavior of saturated concrete under low confinement. For high confinement, the simulations only resemble the experimental results when the fluid compressibility is lower than that of water. Moreover, the effective stress was a relevant variable to describe the behavior of the wet concrete by an intrinsic limit state independent of the degree of saturation.

Le comportement des matériaux multiphasiques couvre une multitude de phénomènes qui suscitent un grand intérêt dans le domaine scientifique et professionnel. Les propriétés mécaniques de ces types de matériau trouvent leur origine dans les phases dont ils sont composés, leur distribution et interaction. Un nouveau modèle hydrodynamique couplé est présenté dans ce travail de thèse, à appliquer à l'analyse de l'hydrodynamique des milieux granulaires saturés. Le modèle associe la méthode des éléments discrets (DEM) pour la modélisation de la phase solide, avec une formulation en volumes finis, à l'échelle des pores (PFV), du problème de l'écoulement. Une importance particulière est donné à la description de l'interaction entre les phases, avec la détermination des forces fluides à appliquer sur chacune des particule, tout en assurant un coût de calcul abordable, qui permet la modélisation de plusieurs milliers des particules en trois dimensions. Le milieux est considéré saturé par un fluide incompressible. Les pores et leur connectivité est basée sur une triangulation régulière des assemblages. L'analogie de cette formulation avec la théorie classique de Biot est présenté. Le modèle est validé par la comparaison des résultats numériques obtenus pour un problème de consolidation d'un sol granulaire avec la solution analytique de Terzaghi. Une approche pour analyser l'hydrodynamique d'un sédiment granulaire est finalement présenté. La reproduction du phénomène de liquéfaction d'un sol est également présentée. / The behaviour of multiphase materials covers a wide range of phenomena of interest to both scientists and engineers. The mechanical properties of these materials originate from all component phases, their distribution and interaction. A new coupled hydromechanical model is presented in this work, to be applied to the analysis of the hydrodynamics of saturated granular media. The model associates the discrete element method (DEM) for the solid phase, and a pore-scale finite volume (PFV) formulation of the flow problem. The emphasis of this model is, on one hand, the microscopic description of the interaction between phases, with the determination of the forces applied on solid particles by the fluid; on the other hand, the model involve affordable computational costs, that allow the simulation of thousands of particles in three dimensional models. The medium is assumed to be saturated of an incompressible fluid. Pore bodies and their connections are defined locally through a regular triangulation of the packings. The analogy of the DEM-PFV model and the classic Biot's theory of poroelasticity is discussed. The model is validated through comparison of the numerical result of a soil consolidation problem with the Terzaghi's analytical solution. An approach to analyze the hydrodynamic of a granular sediment is finally presented. The reproduction of the phenomenon of soil liquefaction is analysed and discussed.

Cette étude porte sur l'influence de la forme des particules sur le comportementmécanique des matériaux granulaires, et les mécanismes de transfert de charge quis'y développent, notamment dans les cas des conduits enterrés. La géométrie desparticules (polygones de forme convexe ou assemblage de particules de forme concaveconstitués de plusieurs disques superposés et indissociables) a été caractérisée par uncoefficient de forme α. Cette étude est basée sur une approche numérique par élémentsdiscrets. Des simulations numériques de l'essai de compression biaxiale montrent queles caractéristiques macroscopiques ou géométriques de l'échantillon granulaire, telque l'angle de frottement macroscopique, la compacité, ou la nature des bandes decisaillement, dépendent fortement du coefficient de forme α et de la convexité ou nonconvexité des grains.Les mécanismes de transfert de charge au dessus d'un conduit souple ont été étudiésexpérimentalement (rouleaux bidimensionnels en condition de déformation plane) etnumériquement (MED). Les expérimentations réalisées montrent que la présence duconduit à peu d'in_uence sur le comportement macroscopique de l'assemblée granulairelors d'une sollicitation biaxiale. Les résultats du modèle numèrique convergentavec les rèsultats expérimentaux et mettent en évidence la présence des mécanismes detransfert de charge au dessus du conduit dont les intensités dépendent du coefficientde forme α. / This study was devoted to the in_uence of grain shape on the mechanical behaviourof granular materials and its e_ect on load transfer over underground pipes. Shapeof convex polygons and concave clumps of discs was generalised with a geometricalparameter α. In the study a Discrete Element Modeling (DEM) approach was used.Biaxial compression of granular assemblies revealed that mechanical and geometricalproperties like porosity, macroscopic friction or shear localisation depends both on αand on grain (non-)convexity.The intergranular load transfer over a _exible pipe was studied both experimentally(2D rods in a plain strain apparatus) and numerically (DEM). The experimentsshowed that the pipe has no signi_cant impact on the macroscopic behaviour of theassembly. The numerical model complied with the experiments and revealed that thearching e_ect in a sheared granular medium exists above the pipe and is magni_edwith the increase of α of the grains.

Les condensateurs multicouches en céramique (Multilayer Ceramic Capacitors, MLCCs) sont des composants passifs clés de l'électronique moderne. Les MLCCs sont constitués d'une alternance d'électrodes métalliques et de couches diélectriques de céramique. Les puces ultraminces sont composées de mélanges de couches micrométriques métalliques et céramiques et d'additifs de céramique de taille nano. Un certain nombre de défauts tels que des fissures, des délaminations des couches et des discontinuités au sein de l'électrode, peuvent survenir dans la fabrication de ces MLCCs ultraminces. Un dispositif expérimental à rayons X (TXM, Transmission X-ray Microscope) avec une résolution spatiale de 30 nm au synchrotron APS (Advanced Photon Source, USA) a été utilisé pour caractériser un volume cylindrique représentatif de Ø 20 µm × 20 µm extrait d'une puce 0603 (1,6 mm × 0,8 mm) au nickel (Ni) + titanate de baryum (BaTiO3, ou BT) avant et après frittage sous argon hydrogéné (2%). La tomographie 3D de la microstructure montre que les discontinuités de l'électrode finale sont liées à des hétérogénéités initiales dans les couches d'électrodes. La radiographie in-situ aux rayons X pendant le frittage (vitesse de chauffage de 10 °C/mn, température de maintien à 1200 °C pendant 1 heure, puis refroidissement à 15 oC/min) d’un volume représentatif d'électrode au palladium (+ baryum-néodyme-titanate) confirme bien que les discontinuités dans l'électrode proviennent de l'hétérogénéité initiale de la poudre, qui est lié à la nature du compactage d'un matériau particulaire. La discontinuité se produit à l'étape précoce du cycle de frittage. A ce stade, l'électrode métallique commence à fritter tandis que le matériau diélectrique peut être considéré comme un substrat inerte qui contraint le frittage de l’électrode.Des études corrélatives utilisant un FIB-SEM (Focused Ion Beam Scanning Electron-microscopie) en tomographie à haute résolution (5 × 5 × 5 nm3) ont été effectuées sur des échantillons MLCC à vert et frittés. Elles confirment que la résolution de la nanotomographie X est suffisante pour étudier l’évolution des hétérogénéités. Cependant la tomographie par FIB permet à la nanotomographie X d’être réinterprétée avec plus de précision. D'autre part, le FIB fournit les paramètres des particules pour les simulations DEM.La méthode des éléments discrets (DEM) a été utilisée pour simuler la microstructure du système multicouche lors du frittage. Tout d'abord, le frittage de la matrice de nickel avec inclusions BT a été simulé en utilisant le code dp3D. Nous avons pu montrer que la vitesse de densification de la matrice diminue avec l'augmentation la fraction volumique d'inclusions et avec la diminution de la taille des inclusions. Pour une fraction volumique donnée, et une taille d’inclusions donnée, une meilleure dispersion des inclusions conduit à un retard plus marqué de la densification du frittage de la matrice de nickel.Le co-frittage de multicouches de BT/Ni/BT a été simulé en tenant compte des informations collectées à partir de la tomographie FIB-SEM à résolution élevée (taille des particules, distribution de taille, hétérogénéités, et pores). On constate que les discontinuités d'électrodes proviennent des hétérogénéités initiales dans le comprimé à vert et se forment au début de frittage sous contrainte. Ces résultats de simulation sont en bonne correspondance avec les observations expérimentales. Une étude paramétrique indique que les discontinuités d'électrodes peuvent être minimisées par l'homogénéisation de la compacité, par l’augmentation de l'épaisseur des électrodes et par l’utilisation d’un chauffage rapide.A partir des résultats expérimentaux et des simulations DEM, une conclusion générale peut être avancée: la discontinuité finale provient de l'hétérogénéité initiale dans les couches d'électrodes et survient à un stade précoce de frittage lorsque les couches diélectriques contraignent les couches d'électrodes / Multi-Layer Ceramic Capacitors (MLCCs) are key passive components in modern electronics. MLCCs consist of alternating metal electrode and ceramic dielectrics layers. In ultrathin MLCC chips, the micrometric layers are composed of submicrometric metal and ceramic powders and nano sized ceramic additives. A number of defects such as cracks, delamination of layers and electrode discontinuity and homogeneity, may arise in the processing of these ultrathin MLCCs. Synchrotron (Advanced Photon Source, Argonne National Laboratory, IL, USA) X-ray based Transmission X-ray Microscope (TXM) with spatial resolution of 30 nm was used to characterize a representative cylindrical volume of Ø 20 µm × 20 µm extracted from a 0603 (1.6 mm×0.8 mm) case size Nickel (Ni)-electrode Barium Titanate (BaTiO3, or BT)-based MLCC before and after sintering under 2H2%+Ar atmosphere. 3D tomographic microstructure imaging shows that the final electrode discontinuity is linked to the initial heterogeneity in the electrode layers. In situ X-ray radiography of sintering (heating ramp of 10 oC, holding at 1200 oC for 1 hour, cooling ramp -15 oC) of a Palladium (Pd) electrode BNT (Barium-neodymium-titanate) based MLCC representative volume was also carried out. It confirmed that discontinuities in the electrode originate from the initial heterogeneities, which are linked to the very particulate nature of the powder material. The discontinuity occurs at the early stage of the sintering cycle. At this stage, the electrode starts to sinter while the dielectric material may be considered as a constraining substrate. Correlative studies using Focused Ion Beam - Scanning Electron Microscope (FIB - SEM) tomography were conducted on green and sintered MLCC samples at high resolution (5 × 5 × 5 nm3). FIB images confirmed that the resolution of the X-ray nCT is sufficient to deal with these heterogeneity evolutions. Still, FIB tomography allows the X-ray nCT to be re-interpreted more accurately. Also, it provides detailed particulate parameters for the DEM simulations.The DEM was used to simulate the microstructure of a multilayer system during sintering. First, the sintering of Nickel matrix with BT inclusions was simulated using the dp3D codes. It is found that the densification rate of the matrix decreases with increasing volume fraction of inclusions and with decreasing size of inclusions. For a given volume fraction and size of inclusions, a better dispersion of the inclusions results in a stronger retardation of the densification kinetics of the nickel matrix.Co-sintering of BT/Ni/BT multilayers was simulated with DEM by taking into account the particulate nature collected from the high resolution FIB nanotomography (FIB-nT) data, such as particle size, size distribution, heterogeneities, pores, and geometry. It is found that the electrode discontinuities originate from the initial heterogeneities in the green compact and form at the early stage of sintering under constraint, in good correspondence to the experimental observations. Parametric studies suggest that electrode discontinuities can be minimized by homogenizing the packing density and thickness of the electrodes and using a fast heating rate.Based on both experimental and DEM simulation results, a general conclusion is reached: the final discontinuity originates from the initial heterogeneity in the electrode layers and occurs at the early stage of sintering when the dielectric layers constrain the electrode layers.

Submitted by Kilvya Braga (kilvyabraga@hotmail.com) on 2018-04-23T14:56:43Z No. of bitstreams: 1 WLADMIR JOSÉ GOMES FLORÊNCIO - DISSERTAÇÃO (PPGEM) 2015.pdf: 4800490 bytes, checksum: f2bc5fbc0347cf5ae8fcd0816a8c0697 (MD5) / Made available in DSpace on 2018-04-23T14:56:43Z (GMT). No. of bitstreams: 1 WLADMIR JOSÉ GOMES FLORÊNCIO - DISSERTAÇÃO (PPGEM) 2015.pdf: 4800490 bytes, checksum: f2bc5fbc0347cf5ae8fcd0816a8c0697 (MD5) Previous issue date: 2015-06-19 / CNPq / Estudou-se a dinâmica do processo de moagem, analisando o movimento da carga de um moinho de bolas em escala de laboratório, a partir de ensaios realizados e a partir da simulação utilizando-se o Método dos Elementos Discretos (MED). Uma adaptação do sistema de transmissão mecânico, do moinho, foi feita com o objetivo de variar a velocidade de rotação entre: 57%, 60%, 65%, 70%, 75% e 80% da velocidade crítica (NC). Ensaios de peneiramento, sem moagem e com moagem, variando o percentual de velocidade crítica do moinho, foram realizados. Com isso estabeleceu-se um ponto de corte de referência na peneira de malha (+30#), cujo objetivo foi determinar a eficiência da moagem a partir da verificação da distribuição granulométrica obtida. O comportamento da dinâmica do processo de moagem foi observado utilizando-se um sistema de filmagem em que foram analisados os deslocamentos e comparados com os obtidos pela simulação computacional em 2D, realizada no software de simulação DEMpack®. Foi desenvolvida uma metodologia com o apoio da simulação computacional da moagem, utilizando-se a posição dos corpos moedores e as características da massa, cujo objetivo foi o de determinar a potência necessária ao movimento do moinho de bolas. Verificou-se ser possível realizar a calibração do modelo de simulação a partir da comparação das imagens obtidas pela filmagem do experimento. O coeficiente de atrito influenciou o comportamento da dinâmica do processo: obteve-se melhores resultados quando se utilizou um coeficiente de atrito mais baixo para simular o comportamento dos corpos moedores e um coeficiente de atrito mais alto para simular o comportamento da carga. / It was studied the dynamics of the grinding process, analyzing the movement of the load a ball mill on a laboratory scale, from tests carried out and from the simulation using the Discrete Elements Method (MED). An adaptation of mechanical transmission system of the mill was taken in order to vary the speed of rotation between: 57%, 60%, 65%, 70%, 75% and 80% of the critical speed (NC). Screening tests without crushing and grinding, varying the percentage of critical mill speed, were performed. With that it was established a reference cutoff point in the mesh sieve (+ 30 #), whose objective was to determine the grinding efficiency from checking the particle size distribution obtained. The dynamic behavior of the milling process was observed using a recording system in which the offsets were analyzed and compared with those obtained by computer simulation of 2D held in DEMpack® simulation software. A methodology with the help of computer simulation of milling was developed, using the position of the grinding media and mass characteristics whose goal was to determine the power required to move the ball mill. It was found to be possible to perform the calibration of the simulation model based on the comparison of images obtained by shooting the experiment. The friction coefficient influence the dynamic behavior of the process: better results are obtained when using a low coefficient of friction to simulate the behavior of the grinding bodies and a higher coefficient of friction to simulate the load behavior.

Diversos materiais de interesse tecnológico podem ser considerados como materiais heterogêneos, onde sua natureza aleatória deve ser considerada para representar corretamente o comportamento não-linear. A avaliação quantitativa do dano em materiais sujeitos a estados de tensão ou deformação tem grande importância devido ao caráter crítico desse fenômeno, que pode crescer de forma abrupta e resultar em uma falha catastrófica da estrutura. Em estudos anteriores, Carpinteri e seus colaboradores apresentaram diferentes aspectos relacionados à caracterização do dano em materiais heterogêneos. Três desses aspectos são discutidos neste trabalho: (i) a proposta do número de fragilidade como medida da fragilidade da estrutura em análise; (ii) a evolução da dimensão fractal em que o processo de dano é desenvolvido; (iii) e os índices globais obtidos pela análise de Emissão Acústica (EA). Neste trabalho, uma versão do método dos elementos discretos formado por barras é utilizada para explorar esses aspectos. Espécimes de material quase-frágil são simulados e, quando possível, os resultados numéricos são comparados com resultados experimentais. Além disso, a discussão dos resultados obtidos é realizada visando compreender o comportamento desse tipo de material, como por exemplo, o fato de que estruturas com diferentes dimensões, porém com o mesmo número de fragilidade, têm comportamentos similares. Ademais, o método numérico empregado é apresentado como uma ferramenta viável para complementar a informação obtida em ensaios experimentais na avaliação do processo de dano. Pelo sinal de EA obtido através do método numérico empregado, obtiveram-se parâmetros para a classificação do tipo de falha e para o cálculo do tensor momento, onde comparando os resultados obtidos pelo modelo numérico e pela EA se observam comportamentos coerentes. / Several materials with technological interest can be considered as heterogeneous materials, where their random nature must be accounted to correctly represent the nonlinear behavior. The quantitative evaluation of damage in materials subjected to stress or strain states have great importance due to the critical nature of this phenomenon, which abruptly can rise to catastrophic failure. In previous studies, Carpinteri and his coworkers have presented different aspects of the damage process characterization in heterogeneous materials. Three of these aspects are discussed in this work: (i) the brittleness number proposal to measure the brittleness level of the analyzed structure, (ii) the relationship of the fractal dimension in which the damage process is developed, (iii) and the global indexes obtained by the Acoustic Emission (AE) analysis. In the present work, a version of discrete element method formed by bars is used to explore these concepts. A set of quasi-brittle material specimen is simulated and, when possible, the numerical results are compared with experimental ones. Moreover, a discussion of the obtained results is carried out aiming to understand the behavior of this kind of material, for instance, the fact that structures with different dimensions, but with the same brittleness number, have similar behavior. In addition, the numerical method is presented as a viable tool to complement information from experimental test on the damage process. From the AE signal obtained by the numerical method, parameters to classify the type of crack and for calculating the moment tensor were obtained, where consistent behaviors are observed by comparing the results of the numerical model and the AE.

L'objectif de ce travail de thèse a été de modéliser avec une méthode aux éléments discrets la fracturation en tension, et plus particulièrement la fragmentation dynamique, sur des matériaux fragiles pour de hautes vitesses de déformation. La fragmentation est un phénomène irréversible, non linéaire et aléatoire. Elle intervient dans de nombreux domaines de la vie courante, quelque soit l'échelle considérée. La modélisation numérique de ce phénomène permettrait une prédiction de certains paramètres statistiques de la fragmentation, comme le nombre de fragments, la taille des fragments, la distribution de la taille des fragments, etc. Pour cette thèse, la Méthode des Éléments Discrets (DEM) s'est révélée être un excellent moyen pour simuler la fracturation en raison de sa nature discrète. Toutefois, une bonne méthode de simulation numérique ne suffit pas à elle seule pour modéliser la fragmentation dynamique. Un critère de rupture doit également être inséré, afin d'introduire un endommagement. Ce critère de rupture s'écrit au niveau d'un lien entre deux particules et il engendre un dommage, en faisant décroître la contrainte locale jusqu'à l'obtention d'une fissuration discrète. Dans un premier temps, un critère de rupture de Camacho-Ortiz |24| a été introduit dans une méthode aux éléments discrets. Ce critère se traduit par un endommagement en fonction d'une ouverture de fissure. Ce premier critère a donné de bons résultats comparé à ceux de |69, 88, 97, 143-147| sur la convergence des paramètres de la fragmentation sur des cas simples, mais nécessite un grand nombre de particules. Dans un second temps, afin d'envisager la modélisation de la fragmentation sur des cas plus complexes en trois dimensions à de hautes vitesses de déformation, un second critère de rupture a été introduit. Ce critère de rupture s'appuie sur une approche physique différente, qui prend en compte l'hétérogénéité des matériaux fragiles avec leurs défauts susceptibles d'évoluer et de provoquer une rupture locale. Pour cela, il fait intervenir une loi probabiliste de Weibull afin d'introduire des défauts par élément de volume. Ce critère a été développé par C. Denoual, P. Forquin et F. Hild |29, 33, 42-44|. Tout d'abord, ce second critère de rupture a été testé sur des cas simples en obtenant une convergence des paramètres statistiques de la fragmentation avec un nombre environ $10$ fois moins important de particules que pour la première méthode. Un cas plus complexe en trois dimensions de modélisation de barre d'Hopkinson en trois dimensions a permis de tester de manière « qualitative » la méthode. / The objective of this thesis work is to model the high-strain rate and dynamic fragmentation of brittle materials using the Discrete Element Method. Fragmentation is an irreversible, nonlinear and random phenomenon.It can be found in many practical applications in engineering and can take place at various length scales. This research work takes advantages of computer simulations to model this phenomenon and to predict a few statistical parameters related to fragmentation including number, size, and size distribution of fragments. To this effect, the Discrete Element Method was found to simulate efficiently fracturing, which is a discrete phenomenon by nature. However, an efficient computer simulation is not sufficient for representing fragmentation. It also needs to account for a rupture criterion and a damage criterion. This rupture criterion is defined at the contact points between particles where it generates a local damage that decreases the local stress until a discrete crack appears. In a first step, the rupture criterion of Camacho-Ortiz |24| has been introduced in the Discrete Element Method. This criterion expresses damage as a function of crack opening. When the local stress reaches a rupture threshold, it decreases linearly with the crack opening until the rupture is obtained. This first criterion gives good results on the convergence of fragmentation parameters in simple cases |69, 88, 97, 143-147|, but requires a great number of particles. In a second step, another rupture criterion has been introduced for simulating the fragmentation of more complex three-dimensional structures for high-strain rates. This rupture criterion is based on a different physical approach that accounts for heterogeneous brittle materials with defects. These defects can evolve and cause local failure. They are introduced per unit volume elementusing a Weibull probability distribution |29, 33, 42-44|. This distribution depends on the local stress until the local stress reaches an activation threshold. After that, the defects propagate and form areas of relaxation in which defect cannot evolve. The damage evolves as these areas of relaxation evolve. This second rupture criterion has been validated in simple cases by examining the convergence of the statistical parameters of fragmentation. Compared to the first criterion, the second criterion requires ten times fewer particles. After, a more complex three-dimensional case, dynamic tensile tests in Hopkinson bars, has been treated.

Quando o concreto é submetido a ações especiais, como cargas cíclicas ou ação de cargas de impacto, modificações em sua composição são necessárias, já que o concreto não apresenta desempenho satisfatório à tração, o que compromete o seu comportamento frente à ação de cargas dinâmicas. Uma alternativa para amenizar esta deficiência consiste em adicionar fibras ao concreto. Estas atuam como reforços à tração, transformando a matriz cimentícia, tipicamente frágil, em um material que apresenta boa resistência residual após a fissuração. Buscando colaborar na avaliação da eficiência de diferentes tipos de fibras, o presente trabalho analisa o comportamento de concretos com fibras de aço, submetidos ao impacto, avaliando a influência do fator de forma, do comprimento e do teor de fibras, assim como do tamanho do agregado. São ainda analisados os efeitos da incorporação de fibras na resistência à compressão, na resistência à tração por compressão diametral, no módulo de elasticidade e na tenacidade dos compósitos. Adicionalmente, é executada uma comparação entre os resultados experimentais e os derivados de um esquema de modelagem da situação de impacto através do uso do método de elementos discretos. Buscou-se, através da modelagem teórica, executar um mapeamento dos danos, provocados por cargas de impacto incrementais, ao longo do tempo, bem como determinar as energias necessárias para levar as placas até a ruptura. Os resultados indicam que a incorporação de fibras de aço não consegue retardar o aparecimento da primeira fissura, mas aumenta significativamente a tenacidade dos compósitos. Fibras mais longas e com maior fator de forma tendem a ser mais eficientes, desde que se supere um teor de fibras mínimo, que neste trabalho ficou em torno de 100.000 fibras/m3, para fibras longas (50-60 mm) e de 400.000 fibras/m3, para fibras curtas, cuja ancoragem é menos eficiente. O método de teste de impacto por queda de esfera se mostrou adequado e sensível, porém o esquema de modelagem numérica testado necessita ser refinado para permitir uma adequada simulação do comportamento de concretos com fibras. / When submitted to special loading patterns, derived from dynamical actions such as cyclic or impact loads, concrete elements need to be reinforced, in order to resist the tensile stresses. A feasible alternative, in such cases, is to incorporate fibers in the concrete matrix. The fibers act as a tensile reinforcement, transforming the fragile cement matrix into a composite with significant post-cracking residual strength. In order to contribute with the data collection about the efficiency of different fiber types, the present research work presents an analysis of the behavior of steel fiber reinforced concretes subjected to impact loads. The work investigates the influences of changes in the shape factor, length and amount of fibers. The effects of these combinations on other basic properties of the composites, such as compression strength, split cylinder tensile strength, Young’s modulus and tenacity is also measured. Additionally, a comparison is made between the experimental results from the impact tests and the estimates obtained from a theoretical model that uses the discrete element method (DEM). This theoretical approach aimed to determine if the model was able to simulate the damage evolution over time generated by the increasing impacts loads, as well as to determine the total energy necessary to crack and break the specimens. The results obtained pointed out that the introduction of steel fibers does not affect the energy for the first crack but increases significantly the tenacity of the composite. Longer fibers, with greater shape factors, tend to be more efficient, provided that the fiber content is sufficiently high. The minimum recommended fiber content, according to the data from this research, may be around 100.000 fibers/m3, for longer fibers (50-60 mm). Or around 400.000 fibers/m3, for shorter fibers, which are not so efficient in terms of anchorage. The impact test method developed was considered adequate, being sensitive to the phenomenon and providing reliable data. The DEM model, however, needs to be refined to be able to deal with fiber concrete composites.