On maturation of crack patterns

TL;DR

This paper models the energy-driven evolution of superficial crack patterns in thin elastic layers, revealing a natural progression towards stable polygonal configurations similar to those observed in geological and biological samples.

Contribution

It introduces a numerical model for crack pattern maturation that captures the evolution towards stable polygonal arrangements, aligning well with experimental observations.

Findings

Crack patterns evolve into stable polygons with mainly five, six, and seven sides.

Pattern properties remain statistically stable despite size changes when contraction is reduced.

The model's results agree with experimental data from geological formations and starch samples.

Abstract

Superficial (two dimensional) crack patterns appear when a thin layer of material elastically attached to a substrate contracts. We study numerically the maturation process undergone by these crack patterns when they are allowed to adapt in order to reduce its energy. The process models the evolution in depth of cracks in geological formations and in starch samples (`columnar jointing'), and also the time evolution (over thousands of years) of crack patterns in frozen soils. We observe an evolution towards a polygonal pattern that consist of a fixed distribution of polygons with mainly five, six and seven sides. They compare very well with known experimental examples. The evolution of one of these `mature' patterns upon reduction of the degree of contraction is also considered. We find that the pattern adapts by closing some of the cracks and rearranging those in the immediate neighborhood. This produces a change of the mean size of the polygons, but remarkably no changes of the statistical properties of the pattern. Comparison with the same behavior recently observed in starch samples is presented.