On maturation of crack patterns

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.

7 pages, 5 figures

References in corpus (2)

• Ferroelastic Dynamics and Strain Compatibility
• Stable propagation of an ordered array of cracks during directional drying

Cited by in corpus (8)

• An Experimental Investigation of the Scaling of Columnar Joints
• Order and disorder in columnar joints
• Universal shapes formed by two interacting cracks
• Drying and cracking mechanisms in a starch slurry
• Diffuse interface approach to brittle fracture
• Modeling plasticity of amorphous composites: Scalar is not enough
• Morphologies of expansion ridges of elastic thin films onto a substrate
• Universal fluctuation of polygonal crack geometry in solidified lava