Statistical properties of fractures in damaged materials

We introduce a model for the dynamics of mud cracking in the limit of of ex tremely thin layers. In this model the growth of fracture proceeds by selec ting the part of the material with the smallest (quenched) breaking thresho ld. In addition, weakening affects the area of the sample neighbour to the crack. Due to the simplicity of the model, it is possible to derive some an alytical results. In particular, we find that the total time to break down the sample grows with the dimension L of the lattice as L-2 even though the percolating cluster has a non-trivial fractal dimension. Furthermore, we o btain a formula for the mean weakening with time of the whole sample.