A Statistical Model of Aggregates Fragmentation

TL;DR

This paper introduces a stochastic lattice-based model for aggregate fragmentation, capturing crack propagation dynamics and reproducing experimentally observed power-law fragment size distributions.

Contribution

It presents a novel statistical model that explains the power-law distribution of fragment sizes during aggregate breakage, supported by analytical and numerical results.

Findings

Mass distribution follows a power-law with exponent -3/2.

Model aligns qualitatively with experimental fragment size distributions.

Crack propagation rules mimic stress-driven crack growth and energy depletion.

Abstract

A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process -- a crack moves against the stress gradient and its energy depletes as it grows. We perform numerical simulations of the model for two-dimensional lattice and reveal that the mass distribution for small and intermediate-size fragments obeys a power-law, F(m)\propto m^(-3/2), in agreement with experimental observations. We develop an analytical theory which explains the detected power-law and demonstrate that the overall fragment mass distribution in our model agrees qualitatively with that, observed in experiments.