Energy dissipation statistics in the random fuse model

TL;DR

This paper investigates the statistical distribution of energy dissipation in the 2D random fuse model under various strain conditions, revealing distinct scaling regimes and the impact of driving rates on energy release patterns.

Contribution

It provides a comprehensive numerical analysis of energy dissipation statistics, identifying different scaling behaviors and effects of driving rates in the random fuse model.

Findings

Energy distribution shows two scaling regimes with a sharp crossover.

At low energies, the probability decays as E^{-1/2}.

At high energies, the decay is approximately E^{-2.75} under quasi-static conditions.

Abstract

We study the statistics of the dissipated energy in the two-dimensional random fuse model for fracture under different imposed strain conditions. By means of extensive numerical simulations we compare different ways to compute the dissipated energy. In the case of a infinitely slow driving rate (quasi-static model) we find that the probability distribution of the released energy shows two different scaling regions separated by a sharp energy crossover. At low energies, the probability of having an event of energy $E$ decays as $\sim E^{-1/2}$, which is robust and independent of the energy quantifier used (or lattice type). At high energies fluctuations dominate the energy distribution leading to a crossover to a different scaling regime, $\sim E^{-2.75}$, whenever the released energy is computed over the whole system. On the contrary, strong finite-size effects are observed if we only consider the energy dissipated at microfractures. In a different numerical experiment the quasi-static dynamics condition is relaxed, so that the system is driven at finite strain load rates, and we find that the energy distribution decays as $\mathcal{P} (E) \sim E^{-1}$ for all the energy range.