| This dissertation explores the numerical tools used for computer simulations and the qualitative micromechanics of granular materials. The discrete element method is an invaluable tool for studying the complex behavior of heterogeneous media like granular matter. Its main shortcoming is its computational intensity, arising from vast difference between the observation and the integration timescales which is particularly acute for macroscopically quasistatic deformation processes.;We first define macroscopically quasistatic processes, on the basis of dimensional analysis. This sets bounds for application of commonly used method for computational acceleration - superficially increased mass of particles. The dimensional analysis of the governing equations also motivates the separation of timescales for the integration of rotations and translations. Take advantage of the difference in characteristic timescales, we develop a two-timescales algorithm based on the concept of inertial manifolds. The algorithm is tested on a biaxial simulation and benchmarked against the accurate short-time step simulation which confirms its accuracy.;We then address the effect of boundary conditions on the deformation of granular material using numerical simulations. Three different boundary conditions are used to simulate biaxial compression: (1) by prescribing a membrane, (2) by imposing pressure directly on the particles and strain for both cases using rigid plates, and (3) by prescribing a penalty function which imposes only strain without the rigid boundary effects. Typically observed properties like persistent shear localization are shown to be an effect of the rigid plates. The effect of the membrane stiffness is examined. The penalty method is shown to yield more uniform stress distributions. Further, the penalty method induces slip bands where deformation localizes, but does not persist in the absence of rigid boundaries.;Granular materials display strain localization as shear bands accompanied by massive rolling. The propagation of rotations, which is closely related to the shear band width, has not been addressed previously. Using numerical techniques, we investigate the effect of force chains on rotation propagation. The transmission of rotations is found to depend on the force network strength and the length scale of the transmissions describes the width of a typical shear band in these materials. |
