Emerging complexity in a simple model of the mechanical behaviour of rocks

TL;DR

This paper introduces a mechanical model for rocks that captures complex behaviors like brittle to ductile transition, damage fractality, and avalanche distributions through elementary damage interactions, viewing the process as a nonlinear complex system.

Contribution

It presents a novel damage interaction model that explains emergent macroscopic behaviors in rocks without explicitly encoding them at the elementary level.

Findings

Reproduces brittle to ductile transition

Shows fractal damage structures

Demonstrates power-law damage avalanches

Abstract

We propose a mechanical model for the behaviour of rocks based on progressive damage at the elementary scale and elastic interaction. It allows us to simulate several experimental observations: mechanical behaviour ranging from brittle to ductile, fractal structure of the damage, powerlaw distribution of the damage avalanches. These macroscopic properties are not incorporated at the elementary scale, but are the results of the interaction between elements. This emerging complexity permits us to consider the strain rock process as a complex system characterized by non-linear dynamics.