# Seismic-like organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks

## TL;DR

This paper demonstrates that seismic-like statistical laws naturally emerge in a model of crack propagation in heterogeneous materials, revealing universal behaviors across various physical systems involving elastic interfaces.

## Contribution

It shows how seismic laws arise in a long-range elastic depinning model, extending understanding of crack dynamics and related phenomena.

## Key findings

- Seismic laws are observed in the crack propagation model.
- Conditions for seismic-like organization are identified.
- Results apply to other systems like wetting and ferromagnetism.

## Abstract

Very often damage and fracture in heterogeneous materials exhibit bursty dynamics made of successive impulse-like events which form characteristic aftershock sequences obeying specific scaling laws initially derived in seismology: Gutenberg-Richter law, productivity law, B\r{a}th's law and Omori-Utsu law. We show here how these laws naturally arise in the model of the long-range elastic depinning interface used as a paradigm to model crack propagation in heterogeneous media. We unravel the specific conditions required to observe this seismic-like organization in the crack propagation problem. Beyond failure problems, the results extend to a variety of situations described by models of the same universality class: contact line motion in the wetting problem or domain wall motion in dirty ferromagnet, to name a few.