Evolving fracture patterns: columnar joints, mud cracks, and polygonal terrain

Abstract

When cracks form in a thin contracting layer, they sequentially break the layer into smaller and smaller pieces. A rectilinear crack pattern encodes information about the order of crack formation, as later cracks tend to intersect with earlier cracks at right angles. In a hexagonal pattern, in contrast, the angles between all cracks at a vertex are near 120${}^{\circ }$. However, hexagonal crack patterns are typically only seen when a crack network opens and heals repeatedly, in a thin layer, or advances by many intermittent steps into a thick layer. Here it is shown how both types of pattern can arise from identical forces, and how a rectilinear crack pattern evolves towards a hexagonal one. Such an evolution is expected when cracks undergo many opening cycles, where the cracks in any cycle are guided by the positions of cracks in the previous cycle, but when they can slightly vary their position, and order of opening. The general features of this evolution are outlined, and compared to a review of the specific patterns of contraction cracks in dried mud, polygonal terrain, columnar joints, and eroding gypsum-sand cements

19 pages, 9 figures, accepted for publication in Phil. Trans. R. Soc. A; theme issue on Geophysical Pattern Formation (to appear 2013)

References in corpus (6)

• An Experimental Investigation of the Scaling of Columnar Joints
• Transition in the pattern of cracks resulting from memory effects in paste
• Universal shapes formed by two interacting cracks
• Imprinting the memory into paste and its visualization as crack patterns in drying process
• Drying and cracking mechanisms in a starch slurry
• Numerical study of drying process and columnar fracture process in granules-water mixtures

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• Periodic necking of misfit hyperelastic filaments embedded in a soft matrix
• Insights into the mechanics of pure and bacteria-laden sessile whole blood droplet evaporation
• An evolution model for polygonal tessellations as models for crack networks and other natural patterns
• Instabilities in Drying Colloidal Films: Role of Surface Charge and Substrate Wettability
• Scaling laws of shrinkage induced fragmentation phenomena