From damage percolation to crack nucleation through finite size criticality

TL;DR

This paper develops a unified theory of fracture in disordered brittle materials, revealing a crossover from percolation to nucleation behavior influenced by disorder and system size, with implications for understanding critical phenomena.

Contribution

It introduces a renormalization group framework that unifies fracture mechanisms, showing how finite disorder leads to a transition from percolation to nucleation fixed points.

Findings

Fracture exhibits mixed first order and continuous characteristics.

Finite size effects induce a crossover with mean-field avalanche scaling.

Critical scaling phenomena depend on disorder strength and system size.

Abstract

We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature. Our renormalization group based approach yields a phase diagram in which the percolation fixed point, expected for infinite disorder, is unstable for finite disorder and flows to a zero-disorder nucleation-type fixed point, thus showing that fracture has mixed first order and continuous character. In a region of intermediate disorder and finite system sizes, we predict a crossover with mean-field avalanche scaling. We discuss intriguing connections to other phenomena where critical scaling is only observed in finite size systems and disappears in the thermodynamic limit.