Many everyday materials, broadly classified as ``particulate media'', are at the heart of many industries and natural phenomena. Examples range from the storage and transport of bulk foods and aggregates such as grains and coal; the processing of pharmaceutical pills and the grinding coffee beans; to the mitigation and cost control of life-threatening events like landslides, earthquakes, and silo failures. The common theme connecting all these phenomena is the mechanical stability of the granular material that arises from interactions at the microscopic level of the grain scale, and how this influences collective properties at the bulk, macroscopic scale. In this dissertation, we present an extensive study of the mechanical properties of a physics-based model of granular particle systems in two dimensions using computer simulations. Specifically, we study the dynamics of an intruder particle that is driven through a dense, disordered packing of particles. This practical technique has the benefit of being amenable to experimental application which we expect will motivate future studies in the area. We find the `microrheology' of the intruder can be traced back to the properties of underlying, original, unperturbed packing, thereby providing a method to characterize the mechanical properties of the material that may otherwise be unavailable. To perform this study, we initially created mechanically stable granular packings of bidisperse discs, for several orders of magnitude of particle friction coefficient $\mu$, over a range in packing densities, or packing fractions $\phi$, in the vicinity of the critical packing fraction $\phi_c$, the density below which the packing is no longer stable. This range in $\phi$ translates to a range in packing pressures $P$, spanning several orders of magnitude down to the $P\rightarrow 0$ limit. For each packing, we apply a driving force to the intruder probe particle and find the critical force $F_{c}$, the minimum force required to induce motion of the probe as it is dragged through the system. We find that $F_{c}(\mu)$ for the different friction packings, scales with the packing pressure $P$ as a power-law according to: $F_{c}(\mu) - F_{c}^{o}(\mu) \sim P^{\beta(\mu)}$. The power-law exponent, $\beta(\mu)$ becomes friction dependent, but approaches the value, $\beta(\mu\to0) = 1.0 \pm 0.1$ in the zero-friction limit. $F_{c}^{o}(\mu)$ is the value of $F_{c}$ in the limit $P \to 0$, that similarly depends on the friction coefficient as, $F_{c}^{o}(\mu) \to 0$, when $\mu \to \infty$. We use this property of $F_{c}^{o}(\mu)$ to characterize the mechanical properties of different frictional packings. Another focus of this study is the `microrheology' of the intruder through force-velocity dependencies in $\mu=0$ systems at different $P$. For this case, the intruder is driven through the packing at a steady-state velocity $$, for driving forces above the critical force $F_D > F_c$. We introduce a scaling function that collapses the force-velocity curves onto a single master curve. This power law scaling of the collapsed curve as $P\rightarrow 0$ is reminiscent of a continuous phase transition, reinforcing the notion that the mechanical state of the system exhibits critical-like features. Furthermore, we also find an alternative scaling collapse of the form: $- \sim (F_{D} - F_{c})^{\alpha}$, where $$ represents a constant velocity term in the limit of small excess forcing, and the critical force $F_{c}$ now appears as fitting parameter that matches our explicit calculations. Thence, we are able to extract $F_{c}$ from a driven probe without a-priori having any knowledge about the state of the system. To further investigate the transition of the system through the different intruder force perturbations, we implemented a coarse graining (CG) technique that transforms our discrete particle interaction force information into continuous stress fields. Through this methodology, we are able to calculate the kinetic and contact stresses as the intruder is driven through the system. We are able to qualify and quantify the directional and distance dependencies of the stress response of the packing due to the driven probe via radial and azimuthal stress calculations. In particular, we find how the stress response not only captures the wake region behind the driven intruder, but also how the stress decays in the forward direction of the intruder, which follows universal behavior.

Les simulations numériques des équations d’Euler deux-fluides réalisé sur des maillages grossiers éliminent les structures fins d’écoulement gaz-solide dans les lits fluidisés. Pour précisément estimer l’hydrodynamique globale de lit, il faut proposer une modélisation qui prend en compte les effets de structure non-résolue. Dans ce but, les maillages sont raffinés pour obtenir le résultat de simulation pleinement résolue ce que les grandeurs statistiques ne modifient plus avec un autre raffinement pour le lit fluidisé périodique dilué gaz-particules sur une géométrie 3D cartésienne et ce résultat est utilisé pour tests "a priori". Les résultats de tests "a priori" montrent que l’équation filtrée de la quantité de mouvement est effectuée mais il faut prendre en compte le flux de la fraction volumique de solide de sous-maille en raison de l’interaction locale de la vitesse du gaz et la fraction volumique de solide pour la force traniée. Nous proposons les modèles fonctionnels et structurels pour le flux de la fraction volumique de solide de sous-maille. En plus, les modèles fermetures du tenseur de sous-maille de la phase dispersée sont similaires aux modèles classiquement utilisés en écoulement turbulent monophasique. Tous les modèles sont validés par test "a priori" et "a posteriori" / Eulerian two fluid approach is generally used to simulate gas-solid flows in industrial circulating fluidized beds. Because of limitation of computational resources, simulations of large vessels are usually performed by using too coarse grid. Coarse grid simulations can not resolve fine flow scales which can play an important role in the dynamic behaviour of the beds. In particular, cancelling out the particle segregation effect of small scales leads to an inadequate modelling of the mean interfacial momentum transfer between phases and particulate shear stresses by secondary effect. Then, an appropriate modelling ac counting for influences of unresolved structures has to be proposed for coarse-grid simu-lations. For this purpose, computational grids are refined to get mesh-independent result where statistical quantities do not change with further mesh refinement for a 3-D peri-odic circulating fluidized bed. The 3-D periodic circulating fluidized is a simple academic configuration where gas-solid flow conducted with A-type particles is periodically driven along the opposite direction of the gravity. The particulate momentum and agitation equations are filtered by the volume averaging and the importance of additional terms due to the averaging procedure are investigated by budget analyses using the mesh independent result. Results show that the filtered momentum equation of phases can be computed on coarse grid simulations but sub-grid drift velocity due to the sub-grid correlation between the local fluid veloc- ity and the local particle volume fraction and particulate sub-grid shear stresses must be taken into account. In this study, we propose functional and structural models for sub- grid drift velocity, written in terms of the difference between the gas velocity-solid volume fraction correlation and the multiplication of the filtered gas velocity with the filtered solid volume fraction. Particulate sub-grid shear stresses are closed by models proposed for single turbulent flows. Models’ predictabilities are investigated by a priori tests and they are validated by coarse-grid simulations of 3-D periodic circulating, dense fluidized beds and experimental data of industrial scale circulating fluidized bed in manner of a posteriori tests