Deformation of Two-Dimensional Amorphous Granular Packings

A microscopic understanding of how amorphous materials deform in response to an imposed disturbance is lacking. In this thesis, the connection between local structure and the observed dynamics is explored experimentally in a disordered granular pillar subjected to a quasi-static deformation. The pillar is composed of a single layer of grains, allowing for easy visualization of all particles throughout the deformation. The addition of a liquid into the system causes capillary bridges form between the grains, making the grains cohesive. The two-dimensionality of the system ensures that the liquid is distributed uniformly throughout the packing, making the cohesive forces between the grains known everywhere. We perform separate experiments to measure these capillarity-induced forces, and we find these measurements to be in excellent agreement with our theoretical model and numerical calculations. In the main experiments presented in this thesis, we explore the quasi-static deformation of granular pillar subjected to uniaxial compression. We find a statistical correlation between the local dynamics, characterized by the deviatoric strain rate, and the local structure, characterized by a new measure, introduced here, akin to a relative free area. This correlation is stronger in the presence of cohesion and indicates that regions that are more (less) well packed relative to their surroundings experience lower (higher) strain rates than their surroundings. The deviatoric strain rate also highlights shear bands within the deforming pillar. These shear bands are transient, moving around as the compression occurs. We have developed a way to identify these extended bands, and we compare the structure within these bands to the structure outside. Preliminary results suggest that these shear bands coincide with paths through the material that tend to have more underpacked regions than other parallel in the vicinity of the shear band

Deformation-Driven Diffusion and Plastic Flow in Two-Dimensional Amorphous Granular Pillars

We report a combined experimental and simulation study of deformation-induced diffusion in compacted two-dimensional amorphous granular pillars, in which thermal fluctuations play negligible role. The pillars, consisting of bidisperse cylindrical acetal plastic particles standing upright on a substrate, are deformed uniaxially and quasistatically by a rigid bar moving at a constant speed. The plastic flow and particle rearrangements in the pillars are characterized by computing the best-fit affine transformation strain and non-affine displacement associated with each particle between two stages of deformation. The non-affine displacement exhibits exponential crossover from ballistic to diffusive behavior with respect to the cumulative deviatoric strain, indicating that in athermal granular packings, the cumulative deviatoric strain plays the role of time in thermal systems and drives effective particle diffusion. We further study the size-dependent deformation of the granular pillars by simulation, and find that different-sized pillars follow self-similar shape evolution during deformation. In addition, the yield stress of the pillars increases linearly with pillar size. Formation of transient shear lines in the pillars during deformation becomes more evident as pillar size increases. The width of these elementary shear bands is about twice the diameter of a particle, and does not vary with pillar size.Comment: 14 pages, 11 figure

Divergence of Voronoi Cell Anisotropy Vector: A Threshold-Free Characterization of Local Structure in Amorphous Materials

Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. We compute the local divergence of these vectors, where positive values correspond to overpacked regions and negative values identify underpacked regions within the material. Distributions of this divergence are nearly Gaussian with zero mean, allowing for structural characterization using only the moments of the distribution. We explore how the standard deviation and skewness vary with the packing fraction for simulations of bidisperse systems and find a kink in these moments that coincides with the jamming transition

Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods

We use machine-learning methods on local structure to identify flow defects—or particles susceptible to rearrangement—in jammed and glassy systems. We apply this method successfully to two very different systems: a two-dimensional experimental realization of a granular pillar under compression and a Lennard-Jones glass in both two and three dimensions above and below its glass transition temperature. We also identify characteristics of flow defects that differentiate them from the rest of the sample. Our results show it is possible to discern subtle structural features responsible for heterogeneous dynamics observed across a broad range of disordered materials