Yes / An experimental study is presented here to understand the stress transmission characteristics under different geometrical arrangements of particulates inside a narrow chamber subjected to axial compression loading. The multi-grain systems considered here are face-centred, simple cubic and poly-dispersed structures, as well as inclusions embedded inside seeded, unseeded and cohesive powder bed of Durcal (calcium carbonate). The distribution of the maximum shear stress, direction of the major principal stress and shear stress concentration factor were obtained using photo stress analysis tomography (PSAT). The results show that the maximum shear stress distribution in the simple cubic structure is chain-like and self-repetitive, i.e., a single grain behaviour is representative of the whole system. This is not the case in the case of other granular packing. In the case of the inclusion surrounded by powder media, the maximum shear stress distribution in the inclusion occurs through ring-like structures, which are different from those observed in the structured granular packing. This tendency increases for an increase in the cohesivity of the surrounding particulates. In the granular systems, the direction of the major principal stress is mostly orthogonal to the direction of loading except in some particles in the random granular packing. In the case of inclusion surrounded by Durcal particulates, the directional of the major principal stress acts along the direction of the axial loading except in the ring region where this tends to be oblique to the direction of axial loading. Estimates of the shear stress concentration factor (k) show that, k tends to be independent of the structural arrangement of granular packing at higher load levels. In the case of inclusion surrounded by powder bed, k for the seeded granulated particulate bed is mostly independent of the external load levels. In the case of unseeded particulate (granulated) bed, a fluctuation in k is observed with the loading level. This suggests that the seeded granules could distribute stresses in a stable manner without much change in the nature of shear stress-transmitting fabric of the particulate contacts under external loading. An increase in the cohesion of particulate bed results in more plastic deformation as shown by the differential shear stress concentration factor. The results reported in this study show the usefulness of optical stress analysis to shed some scientific lights on unravelling some of the complexities of particulate systems under different structural arrangements of grains and surrounding conditions of the inclusions in particulate media.

La mise en place de trains à grande vitesse a rendu de plus en plus cruciale la compréhension et la prévision du comportement dynamique à long terme des voies ferrées. En particulier, le tassement des infrastructures conditionne le coût de maintenance des voies. Ce tassement d’infrastructure est par ailleurs étroitement lié aux propriétés des matériaux constitutifs sollicités par le chargement cyclique. La thèse décrit les résultats obtenus pour la caractérisation d’un matériau de type « micro-ballast » de constitution semblable à celle d’un ballast utilisé en infrastructure ferroviaire, mais de taille de grain réduite (d/D=6/24). L’expérimentation utilise des appareils triaxiaux de deux diamètres F300mm et F100 mm. 1. Essais sous sollicitation monotone: Les essais poussés jusqu’à rupture ont permis de mettre en évidence une courbure de la courbe intrinsèque sous faible niveau de chargement et un effet d’échelle sensible entre les deux tailles d’échantillon. 2. Essais sous chargement cyclique: Le plan d’expériences a permis de prendre en compte l’influence de la fréquence d’application de la sollicitation cyclique, de la pression de confinement, de la charge appliquée et du nombre de cycles. Les résultats obtenus sont interprétés dans le cadre d’une loi de comportement adaptée à l’étude de sollicitations cycliques à grand nombre de cycles / The use of high-speed trains makes it crucial to understand and predict the long term dynamic behavior of railway tracks. In particular, the settlement of infrastructures incurs track maintenance costs. This settlement of infrastructure is besides closely linked to the physical properties of the material, when stressed by a cyclic loading. The thesis describes the experimental results obtained on a so called « micro-ballast » material whose grain properties are similar to those of a ballast used for train tracks, but having reduced grain size (d/D=6/24) . Experiments are performed by using triaxial testing on tow diameters (300 mm and 100 mm). 1. Tests under monotone compression: failure tests provided evidence for a curvature of the failure envelop and a significant scale effect between both sample sizes. 2. Tests under cyclic loading: The experimental plane took into account the influence of the application frequency used for the cyclic loading, the confining pressure, the applied charge and the number of cycles. An interpretation of the results in the context of constitutive equations which can be used for the simulation of a high number of cycles is presented

L'objectif de ce travail de recherche est d'étudier numériquement le transport et le dépôt de particules dans des milieux poreux à l'échelle des pores.Premièrement, un couplage entre la méthode de Boltzmann sur réseau (LBM) et la méthode des éléments discrets (DEM) est réalisé et utilisé pour simuler l'écoulement d'un fluide chargé en particules. La LBM est utilisée pour décrire l'écoulement du fluide autour des fibres tandis que la DEM est utilisée pour traiter la dynamique des particules. Ce couplage est bidirectionnel dans le sens où le mouvement des particules affecte le flux de fluide et réciproquement. Ce modèle nous a permis de prédire l'efficacité de capture et la chute de pression à l'étape initiale du processus de filtration. Le facteur de qualité est également calculé pour déterminer la qualité de filtration.Ensuite, on se focalise sur l'étude de l'efficacité de la capture de fibres de formes de section transversale différentes (circulaire, losange et carrée). Les résultats issus de nos simulations du processus de filtration de la fibre circulaire concordent bien avec les corrélations empiriques. L'impaction des particules sur la face avant de la fibre de forme carrée est plus importante que dans les cas de fibre de formes circulaire et losange. Cependant, en raison d'une chute de pression plus faible, la fibre de section losange présente une meilleure qualité de filtration. Ensuite, les variations du facteur de qualité dues à l'angle d'orientation et au rapport d'aspect des fibres ont été étudiées numériquement pour la forme rectangulaire. Pour chaque cas, on a déterminé la valeur optimale de la zone au vent pour laquelle le facteur de qualité est maximal. La comparaison des valeurs du facteur de qualité obtenues pour les différentes formes de fibre monte une meilleure performance pour la fibre de section carrée orientée avec un angle de π/4.Enfin, l'influence de l'arrangement des fibres sur la qualité de la filtration est analysée en considérant la configuration en quinconce pour les différentes formes. Les simulations conduites pour différentes tailles de particules et différentes valeurs de la densité (particule/air) montent que la fibre de section losange est plus performante en termes de facteur de qualité pour les particules de grande taille et pour les valeurs de densité élevée. La présente étude fournit des pistes pour optimiser le processus de filtration et prédire la qualité de filtration. / The objective of the present research was to numerically investigate the transport and deposition of particles in porous media at the pore scale. Firstly, a developed coupled lattice Boltzmann method (LBM) and discrete element method (DEM) is used to simulate the fluid-particle flow. LBM is employed to describe the fluid flow around fibers whereas DEM is used to deal with the particle dynamics. The corresponding method is two-way coupling in the sense that particle motion affects the fluid flow and reciprocally. It allowed us to predict the capture efficiency and pressure drop at the initial stage of filtration process. The quality factor is also calculated for determining the filtration performance. Secondly, we focus on the study the capture efficiency of single fiber with circular, diamond and square cross-section, respectively. The results of LBM-DEM for filtration process of single circular fiber agree well with the empirical correlation. The impaction of particles on the front side of square-shaped fiber is more favorable than those on circular and diamond cases. However, diamond fiber exhibits a good filtration performance. Then the variations of quality factor due to the different orientation angle and aspect ratio of rectangular fiber were studied using LBM-DEM. For each case, we have found the optimal value of the windward area to which corresponds a maximum value of the quality factor. The comparison of the performance of the different forms of fibers shows that the largest quality factor is obtained for square fiber oriented with angle π/4.Finally, the influence of the arrangement of fiber on filtration performance is analyzed by considering the staggered configuration. Simulations conducted for several particle size and density show that the diamond with staggered array performs better for large particles and high particle-to-fluid density ratio in terms of quality factor. The present study provide an insight to optimize the filtration process and predict filtration performance.

Drivers for sustainability have made it necessary for the construction industry to adapt its traditional processes to become both more efficient and produce less waste. Performance based design and specification in the UK for motorways and trunk roads permits a very flexible approach to pavement design, material selection and performance related testing aimed at utilising materials to their maximum potential. However, it is clear that within the emerging philosophy of using materials that are 'fit for purpose' there are many technical challenges for design and specification. There is a need to develop suitable methods of evaluating materials prior to their being used on site. This project was born out of this requirement, with a particular emphasis on coarse granular materials due to their common role in capping construction and also their unique difficulty for measurement under laboratory conditions due to their large range of particle size. A novel assessment test for coarse capping materials for roads that can be used to indicate their likely short-term in situ performance, under controlled laboratory conditions before construction on site, has been developed during this research programme. Key findings relating to the behaviour of coarse capping materials, the use of stiffness measuring devices and variables that influence the measurement of composite stiffness are discussed in detail. The research highlights the necessity for adequate drainage and protection of foundation materials against increase in water content. When adopting a performance specification the timing of the pavement assessment is critical, both on site and in the laboratory. The performance measured on site should perhaps only be considered as a 'snapshot' relating to the stress state in the material at the time of testing.

The phenomenon of particle retention in granular materials has a wide range of implications. For agricultural operations, these particles can be contaminants transported through the ground that can eventually reach to aquifers, consequently contaminating the water. In oil reservoirs, these particles can be clays that get detached from the rock and migrate with the flow after a change of pressure, plugging the reservoir with the consequent reduction in permeability. These particles can also be traceable nanoparticles, introduced in the reservoir with the purpose of identifying bypassed oil. For all these reasons it is important to understand the mechanisms that contribute to the transport and retention of these particles. In this dissertation the retention of micro and nano size particles was investigated. In saturated model sediments (sphere packs), we analyzed the retention of particles by the mechanism of straining (size exclusion). The analysis focused on experiments reported in the literature in which particles smaller than the smallest pore throats were retained in the sediment. The analysis yields a mechanistic explanation of these observations, by indentifying the retention sites as gaps between pairs of sediment grains. A predictive model was developed that yields a relationship between the straining rate constant and particle size in agreement with the experimental observations. In unsaturated granular materials, the relative contributions of grain surfaces, interfacial areas and contact lines between phases to the retention of colloidal size particles were investigated. An important part of this analysis was the identification and calculation of the length of the contact lines between phases. This estimation of contact line lengths in porous media is the first of its kind. The algorithm developed to compute contact line length yielded values consistent with observations from beads pack and real rocks, which were obtained independently from analysis of high resolution images. Additionally, the predictions of interfacial areas in granular materials were consistent with an established thermodynamic theory of multiphase flow in porous media. Since there is a close relationship between interfacial areas and contact lines this supports the accuracy of the contact line length estimations. Predictions of contact line length and interfacial area in model sediments, combined with experimental values of retention of colloidal size particles in columns of glass beads suggested that it is plausible for interfacial area and contact line to contribute in the same proportion to the retention of particles. The mechanism of retention of surface treated nanoparticles in sedimentary rocks was also investigated, where it was found that retention is reversible and dominated by attractive van der Waals forces between the particles and the rock’s grain surfaces. The intricate combination of factors that affect retention makes the clear identification of the mechanism responsible for trapping a complex task. The work presented in this dissertation provides significant insight into the retention mechanisms in relevant scenarios. / text

L’objectif des travaux présentés dans ce mémoire de thèse est de développer une modélisation numérique de la compaction des poudres composées de particules sécables dans le cadre de la méthode de Dynamique des Contacts en vue d’application au procédé de fabrication du combustible nucléaire. Les particules sont modélisées comme des agrégats cohésifs de fragments potentiels (cellules) de formes polyédriques irréguliers. A l’aide de ce modèle de cellules liées (Bonded Cell Method), nous avons réalisé une étude paramétrique de la résistance des particules par rapport aux paramètres géométriques et mécaniques du modèle. Nos résultats révèlent deux régimes et une mise à l’échelle en loi de puissance de la résistance à la compression en fonction de l’adhésion normale et du rapport entre l’adhérence tangentielle et l’adhésion normale entre cellules. Nous avons optimisé les paramètres du modèle pour la compaction uni-axiale des assemblages d’un grand nombre de particules sécables. Les simulations ont permis d’identifier les mécanismes de compaction et de rupture des particules, et de caractériser l’évolution de la texture et des tailles et formes des fragments. Les résultats obtenus montrent clairement que le processus de compaction est fortement non-linéaire en raison notamment de l’évolution de l’étalement granulométrique qui contrôle la texture et la transmission des contraintes. Enfin, nous avons mené une étude systématique de l’effet de la polydispersité de taille dans le cas de particules sphériques. / The goal of this PhD work is to develop a numerical modeling approach of the compaction of powders composed of crushable particles in the framework of the Contact Dynamics method in view of application to the manufacture process of nuclear fuel. The particles are modeled as cohesive aggregates of potential fragments (cells) of irregular polyhedral shape. Using this Bonded Cell Method, we performed a parametric investigation of the strength of particles with respect to the geometrical and mechanical model parameters. Our results reveal two regimes and a power-law scaling of the compressive strength as a function of the ratio between tangential adherence and normal adhesion between cells. We optimized the model parameters for the uniaxial compression of packings of a large number of crushable particles. The simulations allow us to identify the mechanisms of compaction and fracture of particles, and to characterize the evolution of texture and the sizes and shapes of fragments. Our simulation results clearly show that the compaction process is strongly nonlinear as a consequence of the evolution of particle size distribution, which controls the texture and stress transmission. We also perform a systematic analysis of the effect of size polydispersity in the case of spherical particles.

L'imbibition d’eau pour les matériaux granulaires induit des changements dans la morphologie des ponts capillaires qui passent d'une forme isolée (entre deux grains voisins), à une forme fusionnée (entre plusieurs grains voisins). Ces changements de morphologie des ponts liquides influencent le comportement mécanique de ces matériaux, et peuvent être à l’origine d’instabilités telles que l’effondrement capillaire. La thèse présente une approche expérimentale multi-échelle au laboratoire de l'effondrement capillaire de matériaux granulaires lors d'une imbibition d'eau. L’approche concerne les trois échelles: macroscopique d'un Volume Élémentaire Représentatif, mésoscopique de quelques grains et locale de trois ou quatre grains. À l'échelle macroscopique, des essais d’imbibition, dans une cellule triaxiale, ont permis l'identification et l'analyse du phénomène d'effondrement capillaire en mettant l'accent sur l'évolution des déformations dans le temps. Les essais sont réalisés sur deux types de matériaux granulaires, le premier est un matériau constitué de billes de verre et le deuxième est un sable concassé. Une fraction argileuse est parfois incorporée au matériau. Plusieurs paramètres ont été étudiés en vue de comprendre leurs contributions dans le déclenchement du phénomène d'effondrement comme : la granularité, la teneur en eau initiale, la compacité initiale et le pourcentage des particules argileuses. Aux échelles mésoscopique et locale, on propose une étude expérimentale de caractérisation du comportement mécanique des matériaux granulaires dans le régime pendulaire et funiculaire. On s’intéresse en particulier à l’effet de l’imbibition et de la coalescence sur la force capillaire entre les grains solides à l’échelle considérée. Les essais d'imbibition sont réalisés par ajout d’incréments de volume d’eau aux ponts capillaires. Les résultats relatifs au comportement et à l’effondrement à l’échelle macroscopique lors de l'imbibition d'eau sont discutés en s’aidant des résultats obtenus aux échelles inférieures. / Wetting in granular materials induces changes in the morphology of capillary bridges which pass from an isolated form (between two neighboring grains) to a merged form (between several neighboring grains). These changes in the morphology of the liquid bridges impact the mechanical behavior of these materials, and can lead to instabilities such as capillary collapse. The thesis presents a multi-scale experimental approach in the laboratory of the capillary collapse of granular materials during wetting. The approach concerns the three scales: macroscopic of a Representative Elementary Volume, mesoscopic of several grains and local of three or four grains. At the macroscopic scale, the wetting tests, carried out in a triaxial cell, allowed the identification and the analysis of capillary collapse phenomenon, focusing on the evolution of deformations over time. The tests are carried out on two granular materials, the first is a material made of glass beads and the second is a crushed sand. A clay fraction is sometimes incorporated into the material. Several parameters have been studied in order to understand their contributions to the triggering of the collapse phenomenon, such as: grain size, initial water content, initial compactness and percentage of clay particles. At the mesoscopic and local scales, an experimental study is proposed to characterize the mechanical behavior of a granular materials, in the pendular and funicular regimes. In particular, this study focus on the effect of the wetting and the coalescence of bridges, on the capillary force between grains at the considered scale. Wetting tests were performed by adding water volume increments to the capillary bridges. The results on behavior and collapse at the macroscopic scale during wetting are discussed using the results obtained on the lower scales.

Ce travail de thèse est consacré à l'étude de la corrélation entre la microstructure des matériaux granulaires cimentés, la morphologie des fissures qui peuvent y apparaître et leur perméabilité apparente. Une approche numérique par discrétisation sur réseau a permis de prendre en compte la structure polyphasique hétérogène de ces matériaux et d'étudier les mécanismes qui contrôlent leur comportement et leur rupture. Trois régimes de rupture ont été identifiés en fonction de la fraction volumique de la phase cimentaire et de l'adhésion aux interfaces inclusions/matrice cimentaire. Dans le cadre de la sûreté nucléaire, et dans une optique d'analyse d'étanchéité sur des bétons fissurés, une méthodologie de génération de microstructures représentatives du béton, combinant les fractions volumiques des phases et les distributions des tailles des grains, a été proposée. Cette méthodologie permet d'analyser le réseau de fissures qui peut y apparaitre sous chargement en fonction de la microstructure. En particulier, la tortuosité des fissures est analysée en fonction de la fraction volumique des inclusions et de la distribution de leurs diamètres. Enfin, la perméabilité apparente des des fissures a été étudiée par la simulation de l'écoulement d'un liquide par la methode Lattice Boltzmann. Une corrélation microstructure-tortuosité-perméabilité a été ainsi obtenue. Les outils de modélisation et d'analyse proposés sont suffisamment génériques pour permettre de prendre en compte la complexité microstructurelle d'autres types de matériaux polyphasiques et leurs évolutions. / In this work, we investigate the relationships between the microstructure of cemented granular materials, morphology of cracks that may appear under tensile loading and their apparent permeability. In order to simulate the complexity of the multiphase heterogeneous structure of these materials, a numerical approach based on a lattice discretization was developed and used to study the mechanisms that control their behavior and rupture. Three distinct regimes of crack propagation were evidenced in terms of the combined influence of the matrix volume fraction and particle/matrix adherence. In the context of nuclear safety and in view of analyzing cracked concrete toughness, a methodology is proposed for generating representative microstructures with controlled phase volume fractions and particle size distributions. The cracks obtained under tensile loading are analyzed and a relationship is obtained between the microstructure of concrete and the tortuosity of the cracks. The permeability of cracked numerical microstructures was obtained by the simulation of liquid flow through the cracks by means of the Lattice Boltzmann method. Finally, a microstructure-tortuosity-permeability relation is proposed. The modeling and analysis tools developed in this work are generic enough to be applied to other complex multiphase heterogeneous materials.

Offshore on-bottom pipelines are subjected to cycles of thermal and pressure-induced axial expansion, which can cause them to buckle laterally. For an elegant and cost-effective solution, lateral buckling is allowed in a controlled manner. Of the various design parameters, the soil resistance has the greatest associated uncertainty. Previous studies of lateral pipe-soil interaction have used laboratory model tests and continuum-based numerical methods. However, they are economically and computationally expensive, and have mostly been restricted to pipes on undrained clay. To overcome this limitation, this thesis introduces the distinct element method (DEM) as a novel numerical tool for the study of lateral pipe-soil interaction for partially embedded offshore pipelines on sandy seabeds. The DEM directly models the particulate nature of sandy soils, allowing large displacements of discrete bodies and providing insights into the mechanics of the soil at a particle level. Pipe{soil interaction is studied by DEM analyses through four separate research stages: (i) mechanical characterisation of the soil, (ii) specimen preparation and pipeline implementation, (iii) small displacement pipe loading tests and (iv) large displacement pipe loading tests. The soil is modelled as an assembly of spherical particles exchanging contact forces, energy and momentum when they interact. At the microscopic scale, a novel moment-relative rotation contact law is introduced to account for the irregular shape of real sand grains. At a macroscopic scale, the mechanical behaviour of the sand is calibrated using experimental triaxial test data. Additional work includes the numerical preparation of a soil assembly and the implementation of a pipeline object in the open-source DEM code Yade. A novel specimen preparation technique is developed to assemble a homogeneous sample at a desired relative density. The pipeline is implemented as a cylindrical body with a continuously curved surface and a specific mass. Small displacement loading tests are performed, with a segment of the pipeline interacting with a 3D prismatic soil domain, replicating plane strain conditions. The influence of particle size, domain thickness, loading velocity and damping are investigated. The findings provide valuable recommendations for performing DEM simulations of this problem, balancing numerical accuracy and computational effort. Large displacement loading tests are performed to validate the DEM approach and to obtain detailed insights into the nature of the pipe-soil interaction. Monotonic vertical and lateral loading simulations are quantitatively compared with laboratory results. To replicate realistic loading conditions of the pipeline on the seabed, cyclic large displacement tests are also performed. Both the monotonic and the cyclic tests show a good level of agreement with experimental results obtained in previous research. Moreover, the numerical analyses provide insights into the evolution of particle motion and the failure mechanism within the soil.

Les actionneurs disques sont potentiellement une solution intéressante pour des applications de transport exigeantes, comme le véhicule hybride. Mais la conception de ces actionneurs pour de telles applications se heurte à des difficultés. Une solution réside dans l’utilisation des algorithmes d’optimisations systématique. Encore faut-il disposer, pour utiliser de tels algorithmes, de modèles souples, à la fois précis et rapides. Cette thèse se focalise sur le développement de modèles analytiques fondés sur la résolution formelle des équations de Maxwell, qui permet un bon compromis entre temps de calcul et précision, à condition d’accepter certaines hypothèses simplificatrices, comme la linéarité des matériaux magnétiques. La première partie concerne les modèles électromagnétiques bi-dimensionnels, en développant la structure disque au niveau de son rayon moyen. Pour ces modèles, une attention particulière a été portée sur la modélisation des saillances aussi bien statoriques que rotoriques. Il est montré que l’approximation du coefficient de Carter permet effectivement de déterminer le couple moyen de la machine avec précision. Néanmoins, si on veut déterminer les inductions dans le fer pour calculer les pertes magnétiques, un modèle de l’encochage statorique est nécessaire. Dans un second temps, des modèles tri-dimensionnels analytiques ont été développés, afin de calculer le flux à vide de l’actionneur en prenant en compte les effets des bords et l’effet de courbure. Il est montré que la prise en compte des effets de bords est de première importance dans la modélisation des actionneurs. Par contre, une étude sur l’effet de courbure de la machine disque montre que le développement de l’actionneur au rayon moyen, pourvu que l’on utilise un modèle 3D, n’induit qu’une erreur minime. Un second point concerne l’étude des pertes magnétiques dans les matériaux composites isotropes formés de particules de fer pur isolées les unes des autres, liées puis compressées. En effet, ces matériaux sont très prometteurs en conception de machines électriques, autorisant des parcours de flux tri-dimensionnels, et une isotropie thermique, malgré leur perméabilité magnétique relativement faible. Deux matériaux de la société suédoise Hoganas (l’un dédié aux applications de machines électriques, l’autre à l’électronique de puissance, avec des grains de taille plus faible) ont été caractérisés en termes de pertes magnétiques dans une large gamme de fréquences. Un modèle de pertes classiques a été formulé, en se basant sur des observations microscopiques des échantillons de matériaux. Grâce à l’estimation de ces pertes, une procédure de séparation des pertes magnétiques a pu être mise au point. La déduction du terme de pertes excédentaires a révélé certains mécanismes de magnétisation propres à ces matériaux granulaires, dont des grains ont un comportement magnétique à priori indépendant les uns des autres. Contrairement aux matériaux laminés qui possèdent un nombre d’objets magnétiques actifs relativement bas sur la section de la tôle en champ excédentaire nul, les courants de Foucault permettant une homogénéisation du comportement magnétique lorsque la fréquence augmente, les matériaux granulaires semblent exhiber un comportement tout autre, en présentant au moins un objet magnétique actif par grain en champ excédentaire nul. De telles constatations changent la dépendance des pertes excédentaires en fonction de la fréquence (les pertes excédentaires sont alors proportionnelles à la fréquence f, alors que nous rappelons qu’elles sont proportionnelles à f^0.5 dans la plupart des matériaux laminés). Enfin un début d’optimisation a pu être mené, en se limitant aux modèles électromagnétiques bi-dimensionnels et aux matériaux laminés classiques. Diverses études de sensibilité ont été entreprises. Ce travail se termine par une analyse de l’influence d’une contrainte de puissance apparente sur la géométrie de la machine électrique. / The axial flux actuators are potentially an attractive solution for demanding automotive applications such as hybrid vehicles. However, the design of these actuators for such applications encounters some difficulties: the specifications in terms of torque and speed are complex, conflicting criteria to minimize, such as mass and losses. One solution is to use systematic optimization algorithms. To use these algorithms, flexible models are needed, both accurate and fast. This thesis focuses on developing analytical models based on the formal resolution of Maxwell's equations, which allows a good compromise between computation time and accuracy, if some simplifying assumptions such as linearity of magnetic materials are accepted. The first part concerns the electromagnetic two-dimensional models, developing the axial flux structure at its mean radius. For these models, particular attention was paid to modeling of the salience as well as the rotor stator. It is especially shown that the approximation of the Carter coefficient can effectively determine the average torque of the machine with precision. However, if we want to determine the inductions into the iron parts so as to calculate the magnetic losses, a model of stator slotting is required. In a second step, three-dimensional analytical models were developed to calculate the no-load flux in the actuator, taking into account the edges effects and the curvature effect. It is shown that taking into account the edges effects is important in the modeling of the actuators. A study on the curvature effect of the machine shows that the development of the actuator to the mean radius, provided 3D models are used, is not so wrong. A second point concerns the study of magnetic losses in isotropic composite materials, composed of particles of pure iron insulated from each other, put in a binder, and then compressed. Indeed, these materials are very promising in electric machine design, allowing three-dimensional magnetic flux paths and a thermal isotropy, despite their relatively low magnetic permeability. Two materials of the Swedish company Hoganas (one dedicated to electric machines, the other to power electronics, with grains of smaller size) were characterized in terms of magnetic losses in a wide frequency range . A classical loss model was formulated, based on microscopic observations of samples of materials. With this estimate of the classical losses component, the procedure of loss separation can be carried out. The calculation of the excess loss component revealed some specific magnetization mechanisms in these granular materials, in which grains are independent of each other. Unlike laminated materials that have a number of active magnetic objects relatively low on their section at zero field, (eddy currents allow homogenization of the magnetic behavior when the frequency increases), the granular materials appear to exhibit a totally different behavior, with at least one active magnetic object at zero excess field. This changes the dependence of excess losses as a function of frequency (the excess losses are then proportional to the frequency f, while we remember that they are proportional to f ^ 0.5 in most laminated materials). Finally a pre-optimization has been carried out, with just two-dimensional electromagnetic models, and conventional laminated materials. Various studies, as the control law, or the residual induction of the magnets, have been done. This work finishes with an analysis of the influence of a power constraint on the geometry of the electrical machine.