La fragmentation des matériaux est un phénomène qui entre en jeu dans de nombreux systèmes naturels et industriels, et à différentes échelles. D'un point de vue industriel, la fragmentation est d'une grande importance dans la production de granulats de carrière, qui sont soumis à des critères stricts en termes de tailles et de formes. Néanmoins, les phénomènes à l'origine de la fracture des matériaux restent encore aujourd'hui mal maîtrisés. Les méthodes aux éléments discrets permettent une modélisation des interactions à l'échelle de la microstructure du matériau. Un des avantages de ces méthodes est que la fissure apparaît et se propage dans l'empilement de manière naturelle, sans qu'il soit nécessaire de la décrire par modèles de fissuration.Un modèle aux éléments discrets permettant de représenter la cohésion au sein d'un matériau composé de particules de formes quelconques a été développé durant cette thèse. Des simulations numériques ont été effectuées pour deux types d'empilements représentant soit des matériaux cimentés, soit des matériaux “pleins”. Les résultats obtenus ont permis de confirmer que ce modèle est capable de reproduire le comportement macroscopique de la rupture de matériau fragile. Le modèle a été ensuite appliqué à l'étude de l'influence du positionnement de points de contact externes sur la résistance d'une particule cylindrique. Une étude expérimentale d'impact a été menée et a permis de confirmer ces résultats. Enfin, nous avons appliqué notre approche à la reconstruction de grains issus de données tomographiques. / The fragmentation of materials is a phenomenon which arises in several natural and industrial systems, and for a wide range of scales. From an industrial point of view, the crushing process is very important in the production of aggregates, which are often required to meet high criteria in terms of size and shape. However, the phenomena behind fracture of materials are still not completely understood. The discrete element methods allow to model interactions at the scale of the material micro-structure, by means of simple models. One of the advantages of this kind of methods is the natural way the crack initiates and propagates in the sample, without any need of a crack model. A discrete element model allowing to describe cohesion inside the material composed of particles of arbitrary shapes has been developed in this work. Numerical simulations have been conducted for two kinds of samples describing both cemented and plain materials. The results obtained have shown the ability of the numerical model to reproduce the macroscopic behavior of the fracture of a brittle material. The developed model has been applied to study the influence of the positioning of external contact points on the effective strength of a cylindrical shaped grain. The results have demonstrated an increase of the required force to break the grain depending on the position of the contacts. An experimental study has confirmed the numerical results. Finally, the model has been applied to the building of grains based on tomographic data.

Les structures de sphères creuses appartiennent à la famille des matériaux cellulaires qui ont récemment été étudiés pour leurs multiples propriétés. Dans le cas de cette thèse, le but des sphères creuses est de dissiper l’énergie d’impact d’un oiseau sur un cockpit d’avion. Elles sont développées dans le cadre du projet SAMBA (Shock Absorber Material for Birdshield Application) afin d’optimiser leur énergie spécifique absorbée (J/kg).Dans un premier temps, des essais quasi-statiques (v = 5 mm/min) et dynamiques (v = 2 m/s) de compression uni-axiale sont conduits à température ambiante sur une seule sphère creuse de diamètre 30 mm. Une propagation rapide de fissures macroscopiques est observée. Le formalisme de la Mécanique Élastique Linéaire de la Rupture (MELR) est utilisé pour estimer le taux de restitution d’énergie critique dynamique GIdc du matériau constitutif. La position du sommet de fissure est mesurée pendant la propagation de fissure à l’aide d’une caméra rapide. La Méthode des Éléments Discrets (DEM) permet de simuler la rupture dynamique en implémentant une technique de relâchement des nœuds. Le taux de restitution d’énergie GIdc peut être estimé à partir de l’histoire (position et temps) du sommet de fissure. Le modèle numérique montre que les structures sphériques dissipent une proportion importante de l’énergie par des effets dynamiques. A une même vitesse de propagation, plus l’épaisseur de coque est fine, plus les effets inertiels générés par la rupture sont importants et ce pour une même vitesse de propagation.Le modèle numérique DEM est ensuite employé pour reproduire la rupture dynamique sur une sphère creuse à l’aide d’un critère en contrainte seule ou un critère mixte en contrainte – énergie. Les bons résultats obtenus démontrent la capacité de la DEM à représenter la propagation de fissures en régime dynamique.Finalement, des essais numériques et expérimentaux multi-sphères sont réalisés afin évaluer le comportement des sphères creuses au sein d’un assemblage. / Hollow sphere structure (HSS) belongs to cellular solids that have been studied recently for its multiples properties. In our case, HSS aims to absorb soft impacts energy on an airliner cockpit. HSS is investigated through the SAMBA (Shock Absorber Material for Bird-shield Application) project because of its promises in term of specific energy dissipated (J/kg) during impact.First of all, quasi-static and dynamic (v = 5 mm/min to v = 2 m/s) uniaxial compression tests are conducted at room temperature on a single sphere (D = 30 mm). Rapid crack propagation (RCP) is observed to be predominant at macroscopic scale. The formalism of Linear Elastic Fracture Mechanics (L.E.F.M.) is therefore used to estimate the dynamic energy release rate GIdc . The crack tip location is measured during the crack propagation using a high speed camera. The Discrete Element Method (DEM) is used to simulate the dynamic fracture by implementing the node release technique. The dynamic energy release rate can be determined using an experimentally measured crack history. In spherical structures the numerical results reveal a high proportion of energy dissipated through inertial effects as well as a dependence of the thickness of the hollow sphere over the range of 0.04 mm to 1.2 mm.The DEM model Is then employed to reproduce the RCP according to two failure criterions: a stress criterion and a coupled stress-energy criterion. It reveals to be an interesting way to model the mechanical behavior of brittle materials.Eventually, experimental and numerical multi-spheres tests are performed to evaluate the behavior of brittle hollow spheres within an assembly.

Dans les études expérimentales de la micromécanique des matériaux granulaires, la mesure des forces de contact entre particules est de nos jours toujours un challenge en comparaison avec les outils et techniques bien mieux établis pour la caractérisation cinématique à l'échelle des particules. Cette thèse de doctorat s'attaque à cet ambitieux problème. L'approche proposée implique deux aspects : (i) la caractérisation expérimentale du réseau de contact et de la cinématique à l'échelle des particules, qui peut être réalisée avec des techniques d'imagerie standards ; (ii) une approche numérique capable d'exploiter ces mesures afin de déduire les forces de contact.L'une des contraintes qu'on s'était imposée était de ne s'appuyer que sur la connaissance de la géométrie des particules ainsi que du réseau de contacts pour réaliser la déduction des forces de contact. Trois techniques numériques différentes ont été proposées à cet effet : une méthode basée sur l'élasticité des contacts (CEM), une méthode basée sur la dynamique de contact (CDM) et une méthode basée sur l'équilibre élasto-plastique de l'assemblage granulaire (QSM). Chacune de ces techniques repose sur une approche de la famille des méthodes en éléments discrets ; il s'agit respectivement de le DEM de type Cundall, la dynamique des contacts non régulière, et une approche de calcul statique élastoplastique. La non-unicité de la solution est le principal problème avec les techniques choisies, et elles sont étroitement liées à l’indétermination des forces dans le système.Les trois méthodes sont d'abord présentées et validées en les appliquant à l'estimation des forces dans les systèmes granulaires 2D générés au moyen de simulations DEM explicites. Nous prenons ces simulations comme des expériences "idéales" dans le sens où elles fournissent des données similaires à celles extraites des expériences, mais dépourvues d'erreurs de mesure. Un avantage évident de cette stratégie est d’obtenir des ensembles de forces faisant office de référence faisant foi. Sur cette base, les principaux aspects affectant la détermination des forces peuvent être étudiés. En particulier, le rôle crucial de l'histoire du chargement est mis en évidence et certaines solutions pour les prendre en compte dans la détermination des forces ont été prospectées. Une évaluation de l'influence de l'erreur de mesure a également été réalisée pour prédire l'applicabilité de chaque méthode à des expériences réelles. Une brève analyse de la variabilité des solutions est également fournie.Finalement, des tentatives ont été faites pour déduire des forces issues d’expériences effectuées dans le dispositif 1gamma2epsilon. La cinématique des particules et la connectivité ont été évaluées au moyen de la technique de corrélation d'image numérique. Les avantages et inconvénients des trois méthodes ont été éclaircis. Ils nous conduisent à envisager une utilisation combinée des trois méthodes pour tirer parti de leurs atouts respectifs. À l'avenir, il conviendra de réfléchir à la prise en compte de la stabilité de la solution -- dans l'algorithme de convergence vers une solution -- avec l'espoir de limiter la variabilité des solutions. / In the experimental study of the micro-mechanics of granular materials, measuring inter-particle contact forces is still a challenging task, if compared to the well-established tools and techniques for the kinematic characterisation at particle scale. This doctoral thesis addresses this problem. The proposed approach consists of two parts: an experimental characterisation of the granular network geometry and of particle-scale kinematics, which can be carried out with common imaging techniques such as Digital Image Correlation; a numerical approach aiming to exploit these measurements for the estimation of forces.One imposed constraint was to only make use of the rigid motions of particles, together with the knowledge of the contact network, to infer contact forces. Three different numerical techniques have been proposed to this purpose, referred to as Contact Elasticity Method (CEM), Contact Dynamics-based Method (CDM) and Quasi-Static Method (QSM). Each of these techniques is based on the formulation of common approaches in the family of Discrete Element Methods, respectively the classical Cundall-like DEM, the Non Smooth Contact Dynamics and a quasi-static approach accounting for both contact elasticity and plasticity. It is shown that memory of the history of the packing is the main concern with all the chosen techniques.The three methods are first presented and validated by applying them to the estimation of forces in 2D granular systems generated by means of explicit-time DEM simulations. We refer to these simulations as "ideal" experiments since they are meant to provide the same information that can be extracted from experiments, but without any measurement error. An obvious benefit of this strategy is to get reference force sets that are taken as ground truth. Based on this, the main aspects that affect the determination of forces can be investigated. In particular, the crucial role of history is emphasised here, and some solutions to take it into account in the force inference have been investigated.An assessment of the influence of measurement error has also been carried out, to predict the applicability of each method to real experiments. A short analysis of the variability of the solutions is also provided.Finally, some attempts have been made to infer forces from experiments carried out in the 1gamma2epsilon device. Particle kinematics and connectivity have been assessed by means of the Digital Image Correlation technique.The benefits and drawbacks of the three methods have been demonstrated. They conduct us to envision a combined usage of the three methods. In the future, studying the stability of equilibrium might help reducing the variability of the solutions.

A demanda por estruturas mais leves implica num ganho em economia, porém o aumento de esbeltez da estrutura pode tornar ela susceptível a instabilidade frente a tensões compressivas estáticas ou dinâmicas. A instabilidade acontece em várias escalas da estrutura analisada e pode interagir com outras formas de colapso como a propagação instável de fissuras, problema governado pela mecânica da fratura, pela plastificacão do material, ou por uma combinação dos efeitos citados. Neste contexto, no presente trabalho, se explora a capacidade do método dos elementos discretizados por barras (LDEM) na simulação de problemas de instabilidade estática e dinâmica devido as tensões de compressão. Este método permite simular o sólido como um arranjo de barras com rigidez equivalente ao contínuo que se quer representar. Leis constitutivas não lineares permitem modelar ruptura de forma simples. A equação de movimento resultante da discretização permite formular uma equação de movimento desacoplada que pode ser integrada no domínio do tempo com um método explícito (Método das Diferencias Finitas Centrais). O fato das barras serem rotuladas nos seus extremos e a solução do problema ser obtida de forma incremental permite capturar problemas com não linearidade geométrica, entre eles a instabilidade estrutural frente a tensões compressivas. Como último exemplo se realiza a análise de um painel sanduiche por flexão em três pontos, que é composto por um núcleo de poliuretano, com duas lâminas externas de material compósito, neste caso a instabilidade estrutural está associada a flambagem da camada da lâmina comprimida. Finalmente a potencialidade da metodologia de análise utilizada é discutida. / The demand for lighter structures implies a gain in economy, but the increase in slenderness of the structure may make it susceptible to instability against static or dynamic compressive stresses. Instability occurs at various scales of the analyzed structure and may interact with other forms of collapse such as unstable crack propagation, problem governed by fracture mechanics, plastification of the material, or a combination of the cited effects. In this context, in the present work, we explore the ability of the discrete elements methods by bars (LDEM) in the simulation of problems of static and dynamic instability due to the compression stresses. This method allows to simulate the solid as an arrangement of bars with rigidity equivalent to the continuum that one wants to represent. Constitutive non-linear laws allow simple modeling of rupture. The equation of motion resulting from the discretization allows us to formulate a decoupled motion equation that can be integrated in the time domain with an explicit method (Central Finite Differences Method). The fact that the bars are labeled at their ends and the solution of the problem is obtained in an incremental way allows to capture problems with geometric non-linearity, among them the structural instability against compressive tensions. The last example, the analysis of a sandwich panel by three-point bending, which is composed of a polyurethane core, with two external blades of composite material, in this case the structural instability is associated with buckling of the layer of the compressed blade . Finally, the potential of the analysis methodology is discussed.

Le séchage des matériaux cimentaires et le retrait induit ont des conséquences majeures sur le comportement structurel des dalles et chapes. Le retrait empêché est une des principales causes de la fissuration de ces ouvrages. En sus, si le séchage est unidirectionnel, le retrait différentiel favorise le tuilage qui traduit le soulèvement des coins et des bords des dalles minces. Afin de mieux cerner les phénomènes induits par les gradients d’humidité relative interne, des études expérimentales et numériques ont été menées conjointement, et de nouveaux dispositifs expérimentaux ont été développés. On montre que l’évolution du tuilage dépend principalement de la progression du front de séchage. L’influence prédominante du séchage impose donc de recourir à une cure adaptée. Grâce à sa forte capacité de rétention d’eau, une étude systématique a été conduite sur la chaux en vue d’étudier son potentiel effet de cure. La chaux hydraulique a permis, par son influence sur la microstructure et son effet de cure, de retarder et réduire le tuilage. Sur la base des résultats expérimentaux, deux approches différentes de modélisation du tuilage ont été développées : i/ un modèle analytique continu, et ii/ une modélisation par éléments discrets. Les calculs montrent que des retraits plus importants apparaissent en surface et entraînent une microfissuration qui permet de relaxer les contraintes internes. La chaux semble conduire à une profondeur d’endommagement plus importante, ce qui explique en partie son effet sur l’amplitude du tuilage. L’approche par éléments discrets est capable de reproduire l’évolution du tuilage aussi bien en cinétique qu’en amplitude à partir des seules mesures du retrait différentiel. La chaux s’est aussi révélée bénéfique quand elle est incorporée dans les bétons autoplaçants en agissant à la fois sur le retrait et sur les propriétés viscoélastiques. / Drying of cementitious materials and the induced shrinkage have major consequences on the structural behavior of slabs and screeds. The restrained shrinkage is one of the main causes of cracking. In addition, if the drying is unidirectional, the differential shrinkage leads to curling which is defined as the lifting of the corners and the edges of thin slabs.To understand the phenomena induced by internal relative humidity gradients, experimental and numerical studies have been jointly conducted, and new experimental devices have been developed. It is shown that the evolution of curling mainly depends on the progression of the drying front. The predominant influence of drying therefore requires the use of a suitable method for curing. Thanks to its high water retention capacity, a systematic study has been conducted on lime in order to study its potential curing effect. The hydraulic lime, through its influence on the microstructure and its curing effect, delayed and reduced curling. Based on the experimental results, two different approaches have been developed to model the curling of slabs: i / a continuous analytical model,and ii / a discrete element model. Calculations show that higher shrinkage appears on the surface and causes microcracking that may relax internal stresses. The lime seems to lead to a greater depth of damage, which partly explains its effect on the curling amplitude. The discrete element approach is able to reproduce the evolution of curling both in terms of kinetics and amplitude from the sole measurements of differential shrinkage. Lime is also shown to be beneficial when incorporated into self compacting concretes by acting on both shrinkage and viscoelastic properties.

Acetabular dysplasia, a deformity characterized by the presence of a shallow acetabulum inadequately covering the femoral head, alters force transfer through a joint, causing early-onset hip pain and degeneration. Dysplasia is often treated surgically with a periacetabular osteotomy (PAO), which permits multiplanar acetabular reorientation to stabilize the joint and alleviate pain. PAO alters joint mechanics, including contact stress, which can be assessed via computational methods. This work sought to enhance a discrete element analysis (DEA) model for assessment of the dysplastic hip. The primary focus was on understanding how the gait parameters used to load a DEA model affect the computed contact stress. Several additional studies focused on understanding specific anatomic and demographic factors contributing to the contact stress evaluation were also performed. Implementation of a dysplastic gait pattern to load the DEA models resulted in more cases with improved contact stress and clinical measures after PAO, which concurred with clinical findings. Patient demographics and acetabular and femoral geometry all affected the computed contact stress distributions, emphasizing the importance of proper cohort categorization prior to interpretation of DEA-calculated contact stress. These results indicate that accurate modeling of the particular deformity in this cohort likely requires evaluation of both functional and anatomic differences. These studies improve the ability to realistically model and characterize dysplastic hip contact mechanics. DEA is a valuable tool for assessing contact stress in dysplastic joints, which has the potential to improve patient outcomes by guiding clinicians in non-operative treatment, pre-operative PAO planning, and evaluating intraoperative success.

Osteoarthritis (OA) is the most common type of arthritis, a disease in which inflammation and stiffness of the joints occur. This debilitating disease of the joints currently reigns as the most prevalent among the world's populations. Of particular interest to our group is the study of the biomechanical factors relating to knee OA. Studies have shown that knee OA is related to multiple biomechanical factors, all of which are complexly interrelated. These factors have been seen to produce varied effects on the structures of the knee. This work examines validation of a computational model implementing discrete element analysis, and discusses the potential for large-scale, subject-specific modeling of the knee. In particular, contact stress can be estimated using this technique, and these estimates can potentially be related to OA onset in subjects.

The Discrete Element Method was first introduced by Cundall and Strack (1979) to model granular soils within the context of geotechnical engineering. The material is modeled as a random assembly of discrete elements. Each particle interacts with neighboring particles through contact forces that can be built up and broken at any time. The particles were modeled as discs in 2-D or as spheres in 3-D. Research studies have been conducted to improve the simulation of actual grain shapes. Ashmawy et al. (2003) developed the overlapping rigid clusters (ORC) method to accurately model irregular particle shapes. The idea relies on clumping a number of overlapping discs such that their coincides with that of the actual particle. In this dissertation, experimental verification program is presented. An experimental setup was built and model-grains were manufactured in the laboratory. A numerical simulation for the experimental test was carried out. The numerical and experimental results were compared qualitatively and quantitatively. A good agreement was observed within small displacements ranges. However, results were considerably different at large displacements. Numerical results utilizing the ORC method were closer to the experimental results than those of discs. A sequential and operator-independent procedure, which relies on the ORC concept, was developed. Identical inertial properties between the actual particle and the model were ensured. The new procedure was implemented for rounded and angular particles. The effect of particle shape and angularity on the strength and dilatancy characteristics of granular soils was investigated. A modified shape factor, which relies on the work introduced by Sukumaran and Ashmawy (2001), was developed. A series of pure shear testing simulations was performed on different shape and angularity particle groups. Angularity had a remarkable effect on strength and dilatancy properties compared to shape. The effect of interparticle friction on dilatancy was studied. An attempt was made to use an equivalent interparticle friction to model different particle shapes. It was concluded that there is no one-to-one equivalency between interparticle friction and shape or angularity. Instead, the interparticle friction must be continuously altered as a function of confining pressure and void ratio to achieve the required effect.

The goal of this research is to develop a robust, continuum-based approach for a three-dimensional, Finite Element Method (FEM) simulation of layered geomaterials. There are two main approaches to the numerical modeling of layered geomaterials; discrete or discontinuous techniques and an equivalent continuum concept. In the discontinuous methodology, joints are explicitly simulated. Naturally, discrete techniques provide a more accurate description of discontinuous materials. However, they are complex and necessitate care in modeling of the interface. Also, in many applications, the definition of the input model becomes impractical as the number of joints becomes large. In order to overcome the difficulties associated with discrete techniques, a continuum-based approach has become popular in some application areas. When using a continuum model, a discrete material is replaced by a homogenized continuous material, also known as an 'equivalent continuum'. This leads to a discretization that is independent of both the orientation and spacing of layer boundaries. However, if the layer thickness (i.e., internal length scale of the problem) is large, the classical continuum approach which neglects the effect of internal characteristic length can introduce large errors into the solution. In this research, a full 3D FEM formulation for the elasto-plastic modeling of layered geomaterials is proposed within the framework of Cosserat theory. The effect of the bending stiffness of the layers is incorporated in the matrix of elastic properties. Also, a multi-surface plasticity model, which allows for plastic deformation of both the interfaces between the layers and intact material, is introduced. The model is verified against analytical solutions, discrete numerical models, and experimental data. It is shown that the FEM Cosserat formulation can achieve the same level of accuracy as discontinuous models in predicting the displacements of a layered material with a periodic microstructure. Furthermore, the method is capable of reproducing the strength behaviour of materials with one or more sets of joints. Finally, due to the incorporation of layer thickness into the constitutive model, the FEM Cosserat formulation is capable of capturing complicated failure mechanisms such as the buckling of individual layers of material which occur in stratified media.

The general objective of the research effort reported in this thesis was to develop the knowledge required to optimize the design and operation of solid and semi-solid manure handling and land application equipment. Selected physical and rheological properties of manure products deemed to have an influence on the performances of manure handling and land application equipment were measured and general trends were identified among the measured properties. Relationships were also established between the measured properties and the type of manure as well as its total solids concentration. Field experiments were carried out to evaluate the effects of selected mechanical configurations, operating parameters and product properties on the discharge of manure spreaders. The influence of the type of conveying system (scraper conveyor and system of four augers) and the velocity at which it is operated, the geometry of the holding system and the position of a flow-control gate were all included in the analysis. The discharge rates of the machines as well as the specific energy required by the unloading operations were measured. A numerical modeling method called discrete element method (DEM) was used to create virtual manure, a numerical model of the real product. The measured physical and flow properties were used to develop and validate the virtual manure models. It was found that manure products could successfully be represented in a DE framework and that several parameters defining the contact constitutive model in the DEM had an influence on the behaviour of the virtual products. The DEM was then used to study machine-product interactions taking place in handling and land application equipment. Results from field experiments carried out using various land application equipment were used in the development and validation of the interaction models. The predicted flow rates and power requirements were in good agreement with measured data. The results obtained allowed for a better understanding of the flow of manure products in manure handling and land application equipment. It was found that the constitutive model used for the product influenced the results of the machine-product interactions models. A precision banded applicator under development at the University of Saskatchewan was also modeled. The discharge rate of this equipment is influenced by a number of parameters. The predicted mass distribution across the width of the banded applicator was well correlated to the experimental results. The models developed in this thesis have the potential to become powerful engineering tools for the design of improved machines for the handling and land application of solid and semi-solid manure.