A scaling law to determine cracking lengths in shrinkable granular packings*

Hydrated granular packings can shrink and crack into discrete clusters of grains when dried. Cracking in paint and mud are familiar examples of this phenomenon. Despite its ubiquity, however, an accurate prediction of cracking length scales remains elusive. Here, we uncover the previously overlooked role of individual grain shrinkage in determining crack patterning. We perform experiments with shrinkable hydrogel particles and discrete-element simulations. By incorporating grain shrinkage into classical Griffith crack theory, we obtain a scaling law that quantifies how cluster size depends on the interplay between grain shrinkage, stiffness, and size—in agreement with experiments and simulations. The cracking predictions are applicable to a diverse array of shrinkable granular materials.