Morphological Properties of Shrinkage-Induced Crack Patterns

We investigate morphological properties of shrinkage-induced crack patterns, which are observed such as on cooling lava and drying soil, through numerical simulations of a phase-field (PF) model. Since our PF model does not require any assumptions related to crack nucleations and numerical lattice configurations, we can investigate the pattern formations that purely depend on material/external parameters. We find that our PF model shows various types of pattern formations depending on a shrinkage rate and material constants, and in particular, the shrinkage rate provides a significantly qualitative difference in the pattern formations. Cellular patterns resulting from sequential fragmentations of straight cracks can be observed when using a slow shrinkage rate, while random network patterns resulting from connections of micro cracks that appear simultaneously can be observed when using a rapid shrinkage rate. We quantify the difference of the pattern formations statistically, and explain the origin of the difference on the basis of a simple continuum theory of a thin layer of viscoelastic material.