Granular materials are ubiquitous in nature and indispensable in industry, and it is essential to be able to model granular materials from a continuum perspective in order to obtain predictions for large systems. However, granular materials display several mechanical behaviors that remain challenging to model -- e.g., nonlocal effects, secondary rheology, shear banding, and size segregation in flowing granular mixtures. In this thesis, we address several problems related to continuum modeling and numerical simulation of monodisperse and bidisperse granular systems, which are highlighted below. •Experiments have shown that shear deformation in one region of a granular medium fluidizes its entirety, erasing the yield condition everywhere and enabling slow creep deformation to occur when an external force is applied to a probe in the nominally static regions of the material. We apply a scale-dependent continuum approach -- the nonlocal granular fluidity (NGF) model -- to simulate dense flow in a split-bottom cell with a vane-shape intruder. Our simulations quantitatively predict the experimentally-observed phenomena: (1) the vanishing of the yield condition, (2) an exponential-type relationship between applied torque and creeping rate, and (3) the direction-dependence of the torque/creeping-rate relation. •Recent work has shown that the $\mu(I)$ rheology -- a common local continuum model for steady, dense granular flow -- can display a linear instability under short wavelength perturbations, i.e. Hadamard instability. We demonstrate that the NGF model -- which involves higher-order flow gradients -- successfully regularizes the Hadamard instability. By applying the NGF model in fully nonlinear, finite-element simulations, we also show that the NGF model is capable of predicting diffuse shear localization without mesh-dependence. •We present a finite-element-based numerical approach for a coupled continuum model for flow and size-segregation in bidisperse granular mixtures, which is capable of predicting flow fields and size-segregation dynamics simultaneously for general 3D problems. Our implementation is applied to four canonical inhomogeneous flow problems. We verify the implementation and demonstrate mesh convergence.
Li, Shihong,
"Monodisperse and Bidisperse Dense Granular Flows: ContinuumModeling and Numerical Aspects"
(2020).
Mechanics of Solids Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.26300/5b2f-qr81
