Statistical Modeling for Desiccation Cracking Based on Shape-Dependent Fragmentation Process

We investigate statistical properties of desiccation crack patterns of a thin layer of paste experimentally and theoretically. As an experimental result, we have discovered two characteristic properties associated with the fragment distributions. One is that the fragment size distribution varies with time but can be collapsed into a time-invariant distribution by scaling with its mean, and another is that the aspect ratio distribution also converges with a time-invariant distribution. In order to explain these statistical properties, we have constructed a statistical model based on an elastic theory that describes the dynamics of the paste driven by the shrinkage owing the desiccation. We have confirmed that the statistical model can reproduce the statistical properties observed in the experiments, and have revealed through its analytical calculation that the statistical properties arise from a characteristic scaling relation between a critical stress needed to crack a fragment and the shape of the fragment.