Scaling Law for Cracking in Shrinkable Granular Packings

TL;DR

This paper develops a scaling law that predicts crack patterns in dried granular packings by considering grain shrinkage, stiffness, and size, supported by experiments and simulations.

Contribution

It introduces a novel scaling law extending Griffith theory to account for grain shrinkage effects in granular packings.

Findings

Cluster size depends on grain shrinkage, stiffness, and size.

The scaling law accurately predicts crack patterns across different materials.

Experimental and simulation results validate the theoretical model.

Abstract

Hydrated granular packings often crack into discrete clusters of grains when dried. Despite its ubiquity, accurate prediction of cracking remains elusive. Here, we elucidate the previously overlooked role of individual grain shrinkage---a feature common to many materials---in determining crack patterning using both experiments and simulations. By extending the classical Griffith crack theory, we obtain a scaling law that quantifies how cluster size depends on the interplay between grain shrinkage, stiffness, and size---applicable to a diverse array of shrinkable, granular packings.