Scaling Laws in Shrinkage-Induced Fragmentation

Shrinkage-induced breakup of thin layers of heterogeneous materials is abundant in nature, giving rise to spectacular crack patterns. In the laboratory, this phenomenon is often studied by desiccating thin layers of dense suspensions on rigid substrates, typically resulting in polygonal and highly isotropic crack patterns. To investigate these cracking phenomena, we recently introduced a discrete element model that captures the essential mechanisms of crack nucleation and growth in a layer attached to a substrate. Our analysis reveals two distinct phases in the cracking process: an initial damaged phase, where cracks nucleate and grow while a dominant fragment maintains structural integrity, followed by a fragmentation phase, in which the system breaks up into numerous smaller fragments. The transition between these phases occurs at a well-defined critical damage threshold. Finite-size scaling analyses indicate that this transition resembles a continuous phase transition, with a fully connected crack network emerging at the critical point. The structure of this network is controlled by the adhesion strength to the substrate, and the critical exponents of the damage-to-fragmentation transition agree reasonably well with those of two-dimensional bond percolation.