  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.
