Date of Award

8-1-2011

Degree Name

Doctor of Philosophy

Department

Physics

First Advisor

Silbert, Leonardo

Second Advisor

Byrd, Mark

Abstract

The mechanical properties of granular media are investigated using large-scale computer simulations. We probe the relationship between structural and mechanical properties in static, three dimensional granular packings through the development of a coarse graining procedure that connects the microscopic grain scale properties and a macroscopic continuum level description. We study the manner in which local stresses are redistributed in response to localized force perturbations. We first study stress response in frictionless and frictional shallow, ordered, granular arrays confined by solid boundaries for a range of system sizes. Stress response profiles from inside the packing and at the boundaries for frictional packings agree well with the predictions for the semi-infinite half plane of classical isotropic elasticity theory down to boxes of linear dimensions of approximately forty particle diameters and over several orders of magnitude in the applied force. The response profiles for frictionless packings exhibit transitional regime to strongly anisotropic features with increasing box size. The differences between the nature of the stress response are shown to be characterized by very different particle displacement fields. For unconfined overcompressed face centered cubic (FCC) granular arrays of linear dimensions of approximately sixty particle diameters, stress response propagation is studied. Influence of friction coefficient range is the crossover in stress response for a range of the localized force perturbation. The crossover in stress response is from single-peak stress response of the classical isotropic elasticity prediction to double-peak stress response of the anisotropic elasticity prediction for strong anisotropy in material properties. Stress profiles from the bottom layer of these systems indicate crossover from one-peak to double-peak stress response as the magnitude of force perturbation increases for one friction coefficient. Also, these stress profiles show crossover from double-peak to one-peak stress response as the friction coefficient increases for one force perturbation. For most of the systems stress response near the perturbation source is double-peak, for frictional systems as we go further away from the perturbation source a crossover to one-peak stress response occurs. This crossover is associated with length scales. Length scales associated with the material parameters are investigated. Length scales are defined as a distance at which the crossover occurs for a system. The sole effects of friction coefficients on the stress response transition within the systems are expressed in the power laws between length scales and friction coefficients. A multidimensional phase diagram is constructed to show different regions of one-peak and double-peak stress responses that captures the basic mechanical response properties of granular media.

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