Damage and cracking in thin mud layers

We present a detailed study of a two-dimensional lattice model introduced t o describe mud cracking in the limit of extremely thin layers. In this mode l to each bond in the lattice is assigned a (quenched) random breaking thre shold. Fractures proceed by selecting the 'weakest' part of the material (i .e. the smallest value of the threshold). A local damage rule is also imple mented, by using two different types of weakening of the neighbouring sites , corresponding to different physical situations. We present the results of numerical simulations on this model. We also derive some analytical result s through a probabilistic approach known as run time statistics. In particu lar, we find that the total time to divide the sample scales with the squar e power L-2 of the linear size L of the lattice. This result is not straigh tforward since the percolating cluster has a non-trivial fractal dimension. Furthermore, we present here a formula for the mean weakening of the whole sample during the evolution.