Granular materials are mixtures of discrete, macroscopic particles. They are ubiquitous in nature as well as in everyday life -- in forms such as sand, gravel, pharmaceutical pills, food grains, and industrial powders. However, certain mechanical behaviors of these materials are still beyond the community's understanding, including flow and size-segregation phenomenon. Compared to other common engineering materials such as elastic solids and viscous fluids, modeling of granular flow has remained a persistent challenge, especially from a continuum perspective. This thesis addresses several problems related to the continuum modeling of dense granular materials: * Dense granular heap flows (e.g., avalanches and landslides in nature) consist of a rapid flow regime localized near the free surface and a creeping flow region deep beneath the surface. We apply a scale-dependent continuum approach -- the nonlocal granular fluidity model -- to a representative steady, dense granular heap flow setup and successfully capture the salient features of both regions, which existing continuum models have not been able to simultaneously predict. * The flow threshold of dense granular materials exhibits a size effect that cannot be captured by conventional local, stress-based criteria. Using two-dimensional discrete element method calculations, we explore the configurational generality of the size-dependence of the flow threshold -- i.e., additional strengthening with smaller system size -- and show that the nonlocal granular fluidity model is capable of quantitatively capturing this effect. * Dense granular systems consisting of particles of disparate sizes segregate based on size during flow, resulting in complex, coupled segregation and flow patterns. We study the two driving forces of size-segregation -- pressure-gradients and shear-strain-rate-gradients -- in dense flows of bidisperse disks and show that both the flow fields and the segregation dynamics may be simultaneously captured by coupling a segregation model with the nonlocal granular fluidity model.
Liu, Daren,
"Continuum Modeling of Flow and Size-Segregation in Dense Granular Materials"
(2019).
Mechanics of Solids Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.26300/s8hy-z558
