Inertia and the Critical Scaling of Avalanches in Sheared Disordered Solids
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Date
2013-09-13
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Johns Hopkins University
Abstract
This thesis presents results from molecular dynamic (MD) studies of disordered materials undergoing quasi-static shear at zero temperature. Simulations are performed in both two and three dimensions and with a variety of different damping dynamics. During shear, periods of linearly increasing stress and strain alternate with rapid releases of potential energy and stress, termed avalanches. These avalanches have been found in the past to follow power-law statistics. Avalanches in our simulations are observed to exhibit power-law statistics and obey finite-size scaling relations, indicating critical behavior. In contrast with past studies of the nonequilibrium critical depinning transition at the onset of motion, where inertia was observed to destroy critical behavior, we find that inertia qualitatively changes but does not destroy the observed critical behavior. We can characterize three damping regimes, termed overdamped, underdamped and crossover regimes, by measuring scaling and critical exponents in each regime. During each avalanche, potential energy is transformed to atomic motion, with some particles undergoing large displacements. The distribution of particle displacements during avalanche events is quantified, leading to a relationship between local plasticity and stress release. Over larger strain intervals particle displacements allow us to quantify an effective strain-dependent diffusion and define a diffusion constant. Avalanche events demonstrate notable spatial correlations over strain intervals large compared with the typical inter-event interval. These correlations are measured using the power-spectrum of measures of the local strain field. The correlations are found to be angle dependent and long range in nature, independent of damping rate.
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granular materials, disordered solids, nonequilibrium critical phenomena