The effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions

TL;DR

This study uses molecular dynamics simulations to explore how inertia and spatial dimension influence avalanche behavior in sheared disordered solids, revealing distinct universality classes and scaling laws across different damping regimes.

Contribution

It identifies three universality classes of avalanche scaling in sheared disordered solids and characterizes their behavior in two and three dimensions, highlighting the role of inertia.

Findings

Avalanche size distributions follow a power law over three orders of magnitude.

Scaling exponents are consistent across dimensions within each universality class.

Inertia significantly affects the size and energy of avalanches, especially in the underdamped limit.

Abstract

Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal, quasistatic limit. In all cases the distribution of avalanche sizes follows a power law over at least three orders of magnitude in dissipated energy or stress drop. Scaling exponents are determined using finite-size scaling for systems with thousands to millions of particles. Three distinct universality classes are identified corresponding to overdamped and underdamped limits, as well as a crossover damping that separates the two regimes. For each universality class, the exponent describing the avalanche distributions is the same in two and three dimensions. The spatial extent of plastic damage is proportional to the energy dissipated in an avalanche. Both rise much more rapidly with system size in the underdamped limit where inertia is important. Inertia also lowers the mean energy of configurations sampled by the system and leads to an excess of large events like that seen in earthquake distributions for individual faults. The distribution of stress values during shear narrows to zero with increasing system size and may provide useful information about the size of elemental events in experimental systems. For overdamped and crossover systems the stress variation scales inversely with the square root of the system size. For underdamped systems the variation is determined by the size of the largest events.