Anisotropic fragmentation of shrinking thin layers on a substrate

Layers of dense pastes, colloids attached to a substrate often undergo sequential cracking due to shrinkage stresses caused by desiccation. From the spectacular crack patterns of dried out lake beds through the polygonal ground patterns of permafrost regions to the formation of columnar joints in cooling volcanic lava, shrinkage induced cracking is responsible for a large variety of complex crack structures in nature. Under laboratory conditions this phenomenon is usually investigated by desiccating thin layers of dense colloidal suspensions in a container, which typically leads to polygonal crack patterns with a high degree of isotropy.

It is of great interest how to control the structure of shrinkage induced two-dimensional crack patterns also due to its high importance for technological applications. Recently, it has been demonstrated experimentally for dense calcium carbonate and magnesium carbonate hydroxide pastes that applying mechanical excitation by means of vibration or flow of the paste the emerging desiccation crack pattern remembers the direction of excitation, i.e. main cracks get aligned and their orientation can be tuned by the direction of mechanical excitation.

In order to understand the mechanism of this memory effect, we investigate a fragmentation process of a brittle, cylindrical sample, where the driving force of the cracking coming from a continous shrinkage, which sooner or later destroys the cohesive forces between the structure’s building blocks. Our study is based on a two dimensional discrete element model, where the material is discretised via a special form of the Voronoi-tesselation, with the so-called randomised vector lattice which allows to fine-tune the initial disorder of the system. We assume that the initial mechanical vibration imprints plastic deformation into the paste, which is captured in the model by assuming that the local cohesive strength of the layer has a directional dependence: the layer is stronger along the direction of vibration. We demonstrate that - based on this simple assumption - the model well reproduces the qualitative features of the anisotropic crack patterns observed in experiments. Gradually increasing the degree of anisotropy the system exhibits a crossover from an isotropic cellular structure to an anisotropic one.