La rupture des matériaux quasi-fragiles, tels que les céramiques ou les bétons, peut être représentée schématiquement par la succession des étapes de nucléation et de coalescence de micro-fissures. Modéliser ce processus de rupture est un enjeu particulièrement important lorsque l'on s'intéresse à la résistance des structures en béton, en particulier à la prédiction de la perméabilité des structures endommagées. La démarche choisie est une vision multi-échelle où le comportement global est caractérisé par la mécanique de la rupture, et le comportement local représenté par la méthode des éléments discrets. Le modèle représente la fissuration par des grandeurs généralisées, qui seront définies dans le cadre de la mécanique de la rupture. Afin de prendre en compte l’aspect non linéaire de la fissuration dans les matériaux quasi-fragiles, la cinématique usuelle de la mécanique de la rupture est enrichie par l’ajout de degrés de libertés supplémentaires chargés de représenter la part non linéaire du champ de vitesse. L'évolution du comportement est alors condensé par l'évolution de facteurs d'intensité. Le modèle proposé permet de prédire le comportement lors de chargements de mode mixte I+II proportionnel et non-proportionnel. Enfin, une campagne d'essais visant à caractériser le comportement en fissuration du mortier à été réalisée. Les résultats obtenus montrent un rôle important de la fissuration par fatigue. La méthode de changement d'échelle a également été appliquée sur les champs de vitesse en pointe de fissure, confirmant la représentation du comportement en pointe de fissure par une cinématique enrichie. / Fracture in quasi-brittle materials, such as ceramics or concrete, can be represented schematically by series of events of nucleation and coalescence of micro-cracks. Modeling this process is an important challenge for the reliability and life prediction of concrete structures, in particular the prediction of the permeability of damaged structures. A multi-scale approach is proposed. The global behavior is modeled within the fracture mechanics framework and the local behavior is modeled by the discrete element method. An approach was developed to condense the non linear behavior of the mortar. A model reduction technic is used to extract the relevant information from the discrete elements method. To do so, the velocity field is partitioned into mode I, II, linear and non-linear components, each component being characterized by an intensity factor and a fixed spatial distribution. The response of the material is hence condensed in the evolution of the intensity factors, used as non-local variables. A model was also proposed to predict the behavior of the crack for proportional and non-proportional mixed mode I+II loadings. An experimental campaign was finally conducted to characterize the fatigue and fracture behavior of mortar. The results show that fatigue crack growth can be of significant  importance. The experimental velocity field determined, in the crack tip region, by DIC, were analyzed using the same technic as that used for analyzing the fields obtained by the discrete element method showing consistent results.

Les analyses présentées dans ce mémoire portent sur l'endommagement et la rupture de matériaux hétérogènes. Le mécanisme principal de dégradation est la fissuration à l'échelle la plus petite. Une approche probabiliste s'avère être un outil efficace. Ceci concerne des matériaux à comportement fragile (céramiques, fontes GS sous sollicitation cyclique) ou quasi-fragile (céramiques monolithiques impactées ou renforcées par des fibres longues, ciments renforcés par des fibres longues ou courtes). Le dialogue entre les différentes échelles a d'une part permis de construire des modèles de prévision de l'endommagement et de la rupture. D'autre part, diverses stratégies d'identification des paramètres du matériau ont été mises en oeuvre.

O processo de dano em materiais quasi-frágeis pode ser caracterizado pela perda de isotropia para certos níveis de carga. A localização de deformações, o efeito cooperativo entre regiões danificadas e a avalanche de rupturas são características particulares na medição do dano neste tipo de material. As características mencionadas criam diferentes formas de dissipação de energia, que não são fáceis de representar utilizando métodos baseados na hipótese dos meios contínuos. No presente trabalho uma versão do Método dos Elementos Discretos Formado por Barras é empregado. Neste método a massa do contínuo é concentrada nos nós, os quais são interconectados por barras sem massa. Essas barras possuem uma lei constitutiva bilinear, que é usada para simular a ruptura da estrutura em estudo. A distribuição dos nós permite formar uma treliça tridimensional regular, e a partir dessa discretização espacial é possível chegar a um sistema de equações de movimento, que é resolvido com um esquema explícito de integração numérica (diferenças finitas centrais). Neste método a fratura e a fragmentação são levadas em conta de forma natural, já que as barras que rompem durante o processo são desativadas, respeitando o balanço energético. É possível introduzir heterogeneidade no modelo considerando as propriedades do material como campos espaciais aleatórios com distribuição de probabilidades de Weibull e comprimento de correlação conhecido. Nessa dissertação, é analisado o processo de dano que aparece em estruturas de geometria simples quando solicitadas até o colapso. Diferentes índices são apresentados para realizar a medição do dano. O desempenho desses índices, e a maneira com que eles ajudam na interpretação da evolução do dano, são discutidos nesse trabalho. / The process of damage in quasi-fragile materials is characterized by loss of isotropy for certain load levels. The strain localization, the cooperative effect between damaged regions and the avalanche of ruptures are particular features in measuring the damage in this kind of material. The mentioned features create different forms of energy dissipation, which are not easy to represent with a continuous approach. In the present work a version of the Lattice Discrete Element Method is employed. In this method the mass of the solid is concentrated on node points, which are interconnected by uniaxial elements. These elements have a bilinear constitutive law, which is used to simulate the rupture of the structure under study. The node distribution allows the formation of a regular three-dimensional lattice, and from this spatial discretization it is possible to arrive at a system of equations of motion, which is solved by an explicit numerical integration scheme (central difference). In this method the fracture and fragmentation are taken into account in a natural manner, since the bars that reached their limit strength during the process are disabled of the system, respecting the energy balance. It is possible to introduce heterogeneity in the model considering the material properties as random fields with spatial Weibull probability distribution and known correlation length. In this dissertation, the damage process, which appears in structures of simple geometry, when they are loaded until collapse, is analysed. Different indexes are presented to perform the measurement of the damage. The performance of those indexes, and the way they help in the interpretation of the damage evolution, are discussed in this paper.

O processo de dano em materiais quasi-frágeis pode ser caracterizado pela perda de isotropia para certos níveis de carga. A localização de deformações, o efeito cooperativo entre regiões danificadas e a avalanche de rupturas são características particulares na medição do dano neste tipo de material. As características mencionadas criam diferentes formas de dissipação de energia, que não são fáceis de representar utilizando métodos baseados na hipótese dos meios contínuos. No presente trabalho uma versão do Método dos Elementos Discretos Formado por Barras é empregado. Neste método a massa do contínuo é concentrada nos nós, os quais são interconectados por barras sem massa. Essas barras possuem uma lei constitutiva bilinear, que é usada para simular a ruptura da estrutura em estudo. A distribuição dos nós permite formar uma treliça tridimensional regular, e a partir dessa discretização espacial é possível chegar a um sistema de equações de movimento, que é resolvido com um esquema explícito de integração numérica (diferenças finitas centrais). Neste método a fratura e a fragmentação são levadas em conta de forma natural, já que as barras que rompem durante o processo são desativadas, respeitando o balanço energético. É possível introduzir heterogeneidade no modelo considerando as propriedades do material como campos espaciais aleatórios com distribuição de probabilidades de Weibull e comprimento de correlação conhecido. Nessa dissertação, é analisado o processo de dano que aparece em estruturas de geometria simples quando solicitadas até o colapso. Diferentes índices são apresentados para realizar a medição do dano. O desempenho desses índices, e a maneira com que eles ajudam na interpretação da evolução do dano, são discutidos nesse trabalho. / The process of damage in quasi-fragile materials is characterized by loss of isotropy for certain load levels. The strain localization, the cooperative effect between damaged regions and the avalanche of ruptures are particular features in measuring the damage in this kind of material. The mentioned features create different forms of energy dissipation, which are not easy to represent with a continuous approach. In the present work a version of the Lattice Discrete Element Method is employed. In this method the mass of the solid is concentrated on node points, which are interconnected by uniaxial elements. These elements have a bilinear constitutive law, which is used to simulate the rupture of the structure under study. The node distribution allows the formation of a regular three-dimensional lattice, and from this spatial discretization it is possible to arrive at a system of equations of motion, which is solved by an explicit numerical integration scheme (central difference). In this method the fracture and fragmentation are taken into account in a natural manner, since the bars that reached their limit strength during the process are disabled of the system, respecting the energy balance. It is possible to introduce heterogeneity in the model considering the material properties as random fields with spatial Weibull probability distribution and known correlation length. In this dissertation, the damage process, which appears in structures of simple geometry, when they are loaded until collapse, is analysed. Different indexes are presented to perform the measurement of the damage. The performance of those indexes, and the way they help in the interpretation of the damage evolution, are discussed in this paper.

O processo de dano em materiais quasi-frágeis pode ser caracterizado pela perda de isotropia para certos níveis de carga. A localização de deformações, o efeito cooperativo entre regiões danificadas e a avalanche de rupturas são características particulares na medição do dano neste tipo de material. As características mencionadas criam diferentes formas de dissipação de energia, que não são fáceis de representar utilizando métodos baseados na hipótese dos meios contínuos. No presente trabalho uma versão do Método dos Elementos Discretos Formado por Barras é empregado. Neste método a massa do contínuo é concentrada nos nós, os quais são interconectados por barras sem massa. Essas barras possuem uma lei constitutiva bilinear, que é usada para simular a ruptura da estrutura em estudo. A distribuição dos nós permite formar uma treliça tridimensional regular, e a partir dessa discretização espacial é possível chegar a um sistema de equações de movimento, que é resolvido com um esquema explícito de integração numérica (diferenças finitas centrais). Neste método a fratura e a fragmentação são levadas em conta de forma natural, já que as barras que rompem durante o processo são desativadas, respeitando o balanço energético. É possível introduzir heterogeneidade no modelo considerando as propriedades do material como campos espaciais aleatórios com distribuição de probabilidades de Weibull e comprimento de correlação conhecido. Nessa dissertação, é analisado o processo de dano que aparece em estruturas de geometria simples quando solicitadas até o colapso. Diferentes índices são apresentados para realizar a medição do dano. O desempenho desses índices, e a maneira com que eles ajudam na interpretação da evolução do dano, são discutidos nesse trabalho. / The process of damage in quasi-fragile materials is characterized by loss of isotropy for certain load levels. The strain localization, the cooperative effect between damaged regions and the avalanche of ruptures are particular features in measuring the damage in this kind of material. The mentioned features create different forms of energy dissipation, which are not easy to represent with a continuous approach. In the present work a version of the Lattice Discrete Element Method is employed. In this method the mass of the solid is concentrated on node points, which are interconnected by uniaxial elements. These elements have a bilinear constitutive law, which is used to simulate the rupture of the structure under study. The node distribution allows the formation of a regular three-dimensional lattice, and from this spatial discretization it is possible to arrive at a system of equations of motion, which is solved by an explicit numerical integration scheme (central difference). In this method the fracture and fragmentation are taken into account in a natural manner, since the bars that reached their limit strength during the process are disabled of the system, respecting the energy balance. It is possible to introduce heterogeneity in the model considering the material properties as random fields with spatial Weibull probability distribution and known correlation length. In this dissertation, the damage process, which appears in structures of simple geometry, when they are loaded until collapse, is analysed. Different indexes are presented to perform the measurement of the damage. The performance of those indexes, and the way they help in the interpretation of the damage evolution, are discussed in this paper.

Le travail présenté dans ce document consiste à la réalisation d’outils et de méthodes numériques pour modéliser l’influence de la microstructure des shales à la fois sur les propriétés macroscopiques ainsi que sur le processus de fissuration. La première partie du document est dédiée à la description d’un modèle Éléments Finis 3D (E-FEM) développé pour représenter la microstructure ainsi que la fissuration. Ce modèle fait parti des méthodes à discontinuités. Deux critères de fissuration sont décrits, un en mode I (critère de Rankine) et un second en mode II (critère de Mohr-Coulomb). Ces critères seront utilisés pour caractériser l’influence de la microstructure des shales sur les propriétés macroscopiques à l’aide d’essai de compression triaxiale. Plus particulièrement l’impact de la présence de kérogène dans la roche de schiste sera étudié. La seconde partie présente une méthode de décomposition de domaine (la méthode de mortier) utilisée pour réduire les temps de calcul. Cette méthode a pour avantage de permettre l’utilisation de maillage non conforme, ainsi un raffinement local du maillage est possible. Cette méthode a été intégrée à un code de calcul utilisant la programmation orientée composant et plus particulièrement à l’aide du middleware CTL. Le code de calcul permet de résoudre des problèmes linéaires et non linéaires en utilisant le modèle E-FEM. La dernière partie concerne l'étude de l'influence de la minéralogie sur le processus de fissuration à l'aide du code de calcul parallélisé. Un modèle de couplage hydro-mécanique est ensuite développé et appliqué au calcul de fissuration pour mesurer l'impact de la fissuration sur la perméabilité des shales. / This research study aims at developing tools and numerical methods to model the influence of the microstructure of shales on macroscopic properties and cracking process. The first part of the document is dedicated to the description of a 3D Finite Elements model (E-FEM) developed to represent the microstructure and cracking phenomena. This model is part of the methods with discontinuities. Two cracking criteria are described, a mode I criteria (Rankine) and a mode II criteria (Mohr-Coulomb). These criteria will be used to characterize the influence of the microstructure of shales on the macroscopics properties in triaxial compression testing. More particularly, the impact of the presence of kerogen in the shale rock is considered. The second part presents a domain decomposition method (mortar method) used to reduce computation time. This method has the advantage of allowing the use of non-conforming mesh, so a local mesh refinement is possible. This method has been integrated into a computing code using the component-oriented programming and more specifically the CTL middleware. The computing code solves both linear and nonlinear problems using the E-FEM model. The last part concerns the study of the influence of mineralogy on the cracking process using the parallelized calculation code. A hydro-mechanical coupling model is then developed and applied to the calculation of crack to measure the impact of cracking on the shales permeability.

Le travail effectué tend à représenter le comportement quasi-fragile des matériaux hétérogènes (matériaux à matrice cimentaire). Le principe suivi s'inscrit dans le cadre des approches multi-échelles séquencées où la description des matériaux est faite à une échelle fine (mésoscopique) et l'information est transférée à une échelle plus grande (macroscopique). Les résultats montrent que la prise en compte explicite des hétérogénéités offre des perspectives intéressantes vis-à-vis de l'identification, la compréhension ainsi que la modélisation des comportements macroscopiques. En pratique : à partir d'une description simple de chaque phase ainsi que du comportement des interfaces, un effet structurel est observé, menant à des comportements macroscopiques compliqués. Le travail est donc axé autour de deux problématiques principales. D’un coté, la représentation morphologique des hétérogénéités est produite en utilisant la théorie des excursions de champs aléatoires corrélés, produisant des inclusions de forme aléatoires dont les caractéristiques géométriques et topologiques sont analytiquement contrôlées. D’un autre coté, dans un cadre Elément Fini, un double enrichissement cinématique permet de prendre en compte les hétérogénéités ainsi que le phénomène de dégradation local (microfissuration). En couplant ces deux aspects, le méso-modèle montre des réponses macroscopiques émergentes possédant d'intéressantes propriétés typiques des matériaux à matrice cimentaires telles que : asymétrie de la réponse en traction et en compression, profils de fissurations réalistes ou encore dépendance du comportement vis-à-vis de l’historique du chargement. / The present thesis is part of an approach that attempts to represent the quasi-brittle behavior of heterogeneous materials such as cementitious ones. The guideline followed fits in a sequenced multi-scale framework for which descriptions of the material are selected at a thin scale (mesoscopic or microscopic) and information is transferred to a larger scale (macroscopic). It shows how the explicit representation of heterogeneities offers interesting prospects on identification, understanding and modeling of macroscopic behaviors. In practice, from a simple description of each phases and interfaces behavior, a structural effect that leads to more complex macroscopic behavior is observed. This work is therefore focusing on two main axes. On the one hand, the morphological representation of the heterogeneities is handle using the excursion sets theory. Randomly shaped inclusions, which geometrical and topological characteristics are analytically controlled, are produced by applying a threshold on realizations of correlated Random Fields. On the other hand, the FE implementation of both heterogeneity and local degradation behavior (micro-cracking) are dealt with by a double kinematics enhancement (weak and strong discontinuity) using the Embedded Finite Element Method. Finally, combining both axes of the problematic, the resulting model is tested by modeling cementitious materials at the meso-scale under uniaxial loadings mainly. It reveals an emergent macroscopic response that exhibits several features such as asymmetry of the tension-compression stress-strain relationship, crack patterns or historical-dependency, which are typical of concrete-like materials.

Cette thèse vise à développer un modèle numérique de type lattice permettant de simuler la propagation de fissures sous l’effet d’une injection de fluide dans un milieu hétérogène quasi-fragile. Si la finalité de l'étude concerne l'étude de matrices rocheuses naturelles, dans les différentes parties du manuscrit détaillée ci-après et dans un souci de validation, le modèle a été régulièrement confronté à des résultats expérimentaux obtenus sur des matériaux cimentaires similaires à des roches naturelles en termes de comportements mécaniques et de transport mais présentant des hétérogénéités mieux contrôlées. La première partie du document est dédiée à l'étude du processus de fissuration caractéristique des matériaux quasi-fragiles présentant une zone d'élaboration. Un outil d'analyse statistique basé sur les fonctions de Ripley et permettant d'extraire une longueur caractéristique à partir d'un nuage de points -- lieux d'un endommagement mécanique -- et présenté. Il est ensuite utilisé dans le cadre d'essais numériques et expérimentaux de rupture par flexion 3 points sur des éprouvettes de bétons. Les résultats montrent que le modèle numérique de type lattice est capable de rendre compte à la fois du processus global de fissuration mais également du processus local de fissuration. Par ailleurs, cet outil permet également de montrer l'influence du mode de sollicitation sur le développement de l'endommagement au sein d'une structure. La deuxième partie du document présente une loi de comportement élasto-plastique endommageable représentative du comportement de joints. L'originalité du modèle réside dans le couplage entre l'endommagement sous sollicitation normale et la plasticité sous sollicitation tangentielle. Cette nouvelle loi permet de reproduire correctement des résultats d'essais de cisaillement indirects effectués sur des joints de plâtre séparant des épontes en mortier alors qu'un modèle de Mohr-Coulomb classique ne le permet pas. La troisième partie est dédiée à l'introduction d'un couplage hydromécanique complet dans le modèle lattice utilisé précédemment. Le couplage hydromécanique est introduit au travers du comportement poromécanique du milieu basé sur une description mécanique-hydraulique duale et intrinsèque du modèle lattice. La contrainte totale fait le lien entre la contrainte mécanique du lattice mécanique et la pression de pore du lattice hydraulique au travers du coefficient du Biot du milieu alors que la perméabilité locale pilotant le gradient de pression hydraulique est indexée sur les ouvertures locales de fissures estimées au travers du lattice mécanique. Les résultats obtenus par ce modèle hydro-mécanique dual ont été confrontés à des solutions analytiques données dans la littérature pour des fissures de type "bi-wings", et il est montré que les deux approches sont cohérentes pour une fissure parfaitement rectiligne. Après les différentes étapes de validation du modèle présentées dans les parties précédentes, la quatrième et dernière partie est dédiée à la simulation numérique du couplage hydromécanique sous-jacent à la propagation libre d'une fissure propageant sous l'effet d'une injection de fluide et de son interaction avec un joint rocheux naturel. Les trajets de fissuration, non maillés a priori, et les profils de pression au sein de la matrice poreuse sont obtenus et comparés en fonction de l'inclinaison du joint rocheux. Par ailleurs, le traitement statistique concernant les lieux d'endommagement développé en première partie est repris ici afin de caractériser l'évolution des longueurs de corrélation entre point s'endommageant au cours de la propagation de la fissure et de son interaction avec le joint. Il est montré que le modèle hydromécanique lattice permet de représenter différent mécanismes de ré-initiation de fissure à partir d'un joint suivant son inclinaison. / This research study aims at developing a lattice-type numerical model allowing the simulation of crack propagation under fluid injection in a quasi-brittle heterogeneous medium. This numerical tool will be used to get a better understanding of initiation and propagation conditions of cracks in rock materials presenting natural joints where the coupling between mechanical damage and fluid transfer properties are at stake. If the final goal of the study does concern natural rocks, the model has been validated by different comparisons with experimental results obtained on cementitious materials mimicking natural rocks in term of mechanical and transport behaviours but presenting heterogeneities which are better controlled. The first part of the manuscript presents a general state of the art. The second part of the manuscript is dedicated to the study of crack propagation in quasi-brittle materials where a significant fracture process zone is evolving upon failure. Only the solid phase is studied here and a statistical tool based on Ripley’s functions is adapted in order to extract a characteristic length representative of the correlations appearing between a set of point undergoing mechanical damage. This tool is then used in the context of numerical and experimental fracture tests on 3 point bending concrete beams. The results show that the lattice-type numerical model is able to capture the global fracture process – in term of force vs. crack opening mouth displacement – but also the local fracture process – in term of dissipated energy and correlation length evolution between damage points. Moreover, this statistical tool shows how the solicitation mode may influence the development of damage within a structure. The third part presents a new elasto-plastic damage constitutive law for joint modelling. The originality of the model lies in the coupling between mechanical damage under normal strain and plasticity under tangential strain. This new constitutive law is able to reproduce indirect shear experimental tests performed on mortar specimens presenting a plaster joint where a classical Mohr-Coulomb criterion fails. The fourth part is dedicated to the representation of the full hydro-mechanical coupling within the lattice-type numerical model. The hydro-mechanical coupling is introduced through a poromechanical framework based on the intrinsic and dual hydro-mechanical description of the lattice model, which is based on a "hydraulic" Voronoï tessellation and a "mechanical" Delaunay triangulation. The total stress links the mechanical stress and the pore pressure through the Biot coefficient of the medium whereas the local permeability, which drives the hydraulic pressure gradient, depends on the local crack openings. The numerical results are compared with analytical solutions from the literature for "bi-wings" shape cracks and it is shown that both approaches present similar results for a perfect straight crack. Once the lattice-model has been successfully validated within the former parts of the manuscript, its fifth and last part is dedicated to the numerical simulation of the fully hydro-mechanical coupling problem of a free crack propagation due to fluid injection and its interaction with a natural joint in an heterogeneous rock medium. Different crack paths, which are not pre-meshed a priori, and different pressure profiles are obtained and compared for different joint inclinations. Finally, our statistical tool, which has been primarily developed for the analysis of the failure behaviour of the solid phase, is used to characterise the evolution of correlation lengths between points undergoing damage upon the crack propagation and its interaction with a natural joint. It is shown that the hydro-mechanical lattice model is able to represent different mechanism of crack stop and restart from a joint depending on its inclination.

É uma verdade incontestável que a fadiga constitui um dos problemas mais críticos em engenharia, especialmente em estruturas formadas por materiais dúcteis. Por essa razão, uma grande quantidade de métodos e estudos tem sido desenvolvida para tratar deste problema. No entanto, no caso de materiais quase frágeis como concreto, rochas cerâmicas e alguns tipos de materiais compostos, o efeito que cargas oscilantes produzem sobre estes materiais é menos conhecido e aparentemente também menos crítico. No presente trabalho, se utiliza uma versão do método dos elementos discretos formado por barras para explorar as possibilidades do mesmo na simulação do efeito de fadiga em materiais quase frágeis. Simulações sobre corpos de prova simples são apresentadas e vários aspectos deste estudo são discutidos, entre eles: influência da escala, influência da aleatoriedade nas propriedades do material simulado e se a lei de crescimento prevista por Paris (1961) se apresenta nas simulações realizadas. Finalmente, nas considerações finais, são salientadas as possibilidades que se abrem ao aplicar o modelo de elementos discretos apresentado no estudo de materiais quase frágeis submetidos à ação de cargas oscilantes. / It is an unquestionable truth that fatigue consists in one of the most critical problems of engineering, especially in ductile material structures. For that reason, a great amount of methods and studies has been developed to deal with this matter. However, when it comes to quasi brittle materials like concrete, ceramic stones and a few kinds of composites, the effect of cyclic loading on these materials is less well known, and apparently also less critical. In this work, a version of the discrete elements method formed by bars is applied to explore the possibilities of its use on simulating the effect of fatigue over quasi brittle materials. Simulations are presented over simple test specimens and several features of this study are discussed, among them: the influence of specimen scale, the influence of random distribution on material properties and if crack growth laws previewed by Paris, (Paris et al., 1961) are verified in the performed simulations. In the final considerations, the possibilities brought by applying the discrete elements method in this study of quasi brittle materials submitted to cyclic loading are highlighted.

É uma verdade incontestável que a fadiga constitui um dos problemas mais críticos em engenharia, especialmente em estruturas formadas por materiais dúcteis. Por essa razão, uma grande quantidade de métodos e estudos tem sido desenvolvida para tratar deste problema. No entanto, no caso de materiais quase frágeis como concreto, rochas cerâmicas e alguns tipos de materiais compostos, o efeito que cargas oscilantes produzem sobre estes materiais é menos conhecido e aparentemente também menos crítico. No presente trabalho, se utiliza uma versão do método dos elementos discretos formado por barras para explorar as possibilidades do mesmo na simulação do efeito de fadiga em materiais quase frágeis. Simulações sobre corpos de prova simples são apresentadas e vários aspectos deste estudo são discutidos, entre eles: influência da escala, influência da aleatoriedade nas propriedades do material simulado e se a lei de crescimento prevista por Paris (1961) se apresenta nas simulações realizadas. Finalmente, nas considerações finais, são salientadas as possibilidades que se abrem ao aplicar o modelo de elementos discretos apresentado no estudo de materiais quase frágeis submetidos à ação de cargas oscilantes. / It is an unquestionable truth that fatigue consists in one of the most critical problems of engineering, especially in ductile material structures. For that reason, a great amount of methods and studies has been developed to deal with this matter. However, when it comes to quasi brittle materials like concrete, ceramic stones and a few kinds of composites, the effect of cyclic loading on these materials is less well known, and apparently also less critical. In this work, a version of the discrete elements method formed by bars is applied to explore the possibilities of its use on simulating the effect of fatigue over quasi brittle materials. Simulations are presented over simple test specimens and several features of this study are discussed, among them: the influence of specimen scale, the influence of random distribution on material properties and if crack growth laws previewed by Paris, (Paris et al., 1961) are verified in the performed simulations. In the final considerations, the possibilities brought by applying the discrete elements method in this study of quasi brittle materials submitted to cyclic loading are highlighted.