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Granular materials are prevalent ubiquitously in nature and everyday life. They are commonly used as raw materials in various industries; their processing, handling and storage is far from understood, posing many open challenges for scientific community. Granular materials behave in a different manner than usual solids and fluids, exhibit unique mechanical properties. For example, granular matter can flow when shaken or poured through a hopper, but jams (solidifies) when the shaking intensity or pouring rate is lowered. For these reasons, they have attracted significant scientific interest over the past few decades. The bulk behavior of granular materials depends on their constituent particles and they interact through contact forces. The major objective of this work is to model the micro-macro transition towards understanding their micro-based macro-behavior. In the first part of this dissertation, simulational results using the Discrete Element Method (DEM) of idealized, frictionless, disordered sphere packings of dense granular materials are presented. The goal is to gain a better understanding of the mechanical behavior of granular matter. A guideline is presented for calibrating a simplified theoretical anisotropy continuum model using the results from isotropic and deviatoric element tests. This calibrated model (parameters) is then able to predict qualitatively the macroscopic behavior of granular assemblies for an independent uniaxial compression test. Afterwards, the micro- and macro-mechanical behavior of similar assemblies emphasizing the effect of polydispersity is analyzed. As main finding, a relationship for the jamming volume fraction (and other parameters) as functions of the polydispersity and the deformation modes is obtained. The goal of the second part of this dissertation, is to link the elastic moduli (small strain stiffness) with the state variables of the polydisperse anisotropic material, in order to predict the constitutive macroscopic behavior along a generic deformation path. This is achieved by applying small perturbations to various static equilibrium states that previously experienced different history, and by investigating the effect of volume fraction, stress state and microstructure (fabric) on the bulk elastic response of the material. A fully calibrated elastic-plastic anisotropy constitutive model is the major result and is able to predict quantitatively the evolution of pressure, shear stress and deviatoric fabric for an independent cyclic pure shear test. Finally, in the last chapter, based on the study of soft, frictionless, polydisperse spheres, a quantitative model is proposed for how the jamming density changes with history; this quantity is then representing a memory state-variable of the system. One can explain how the packing efficiency increases logarithmically slow under gentle “tapping” or repeated compression, and, in contrast, how it rapidly decreases for shear deformations. By modifying the anisotropy continuum model, and adding the memory (history) dependent jamming point, its predictive power is shown to quantitatively explain many more real-world observations

Micro-macro and jamming transition of polydisperse granular materials