Model inspired by population genetics to study fragmentation of brittle plates

TL;DR

This paper introduces a population genetics-inspired model to analyze brittle plate fragmentation, capturing experimental statistical features without complex physics simulations, and predicting testable physical behaviors.

Contribution

The paper presents a novel random capability growth model inspired by population genetics that effectively describes fragmentation patterns of brittle plates.

Findings

Reproduces composite scaling laws observed in experiments.

Identifies small critical exponents u in fragment-size distributions.

Predicts crack patterns consistent with experimental observations.

Abstract

We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence of (i) composite scaling laws, (ii) small critical exponents \tau associated with the power-law fragment-size distribution, and (iii) the typical pattern of cracks. The proposed computer simulations do not require numerical solutions of the Newton's equations of motion, nor several additional assumptions normally used in discrete element models. The model is also able to predict some physical aspects which could be tested in new experiments of fragmentation of brittle systems.