Avalanche Size Scaling in Sheared Three-Dimensional Amorphous Solid

TL;DR

This study investigates the size distribution and fractal nature of plastic rearrangement avalanches in a simulated 3D amorphous solid, revealing non-trivial scaling behavior and complex avalanche geometries.

Contribution

It provides new insights into the scaling laws and fractal characteristics of avalanches in three-dimensional amorphous solids, extending understanding beyond 2D models.

Findings

Event sizes scale as L^{3/2}

Avalanches are fractal in shape

Distribution of event energies is exponential

Abstract

We have studied the statistics of plastic rearrangement events in a simulated amorphous solid at T=0. Events are characterized by the energy release and the ``slip volume'', the product of plastic strain and system volume. Their distributions for a given system size $L$ appear to be exponential, but a characteristic event size cannot be inferred, because the mean values of these quantities increase as $L^{\alpha}$ with $\alpha \sim 3/2$. In contrast to results obtained in 2D models, we do not see simply connected avalanches. The exponent suggests a fractal shape of the avalanches, which is also evidenced by the mean fractal dimension and participation ratio.