We study a theoretical model of mud cracks, that is, the fracture patterns resulting from the contraction with drying in a thin layer of a mixture of granules and water. In this model, we consider the slip on the bottom of this layer and the relaxation of the elastic field that represents deformation of the layer. Analysis of the one-dimensional model gives results for the crack size that are consistent with experiments. We propose an analytical method of estimation for the growth velocity of a simple straight crack to explain the very slow propagation observed in actual experiments. Numerical simulations reveal the dependence of qualitative nature of the formation of crack patterns on material properties.

• Received 28 May 1999

DOI:https://doi.org/10.1103/PhysRevE.60.6449