Model for surface cracking

We introduce a network model to study the cracking of the surface of a material subjected to an imposed strain along one boundary, or to a surface shrinkage induced by drying or cooling. The model we study is an electrical analog of the mechanical problem, and consists in a network of fuses whose breaking thresholds are randomly distributed. The coupling with a substrate, where a uniform electric field is applied, models the hindering to shrinking of the mechanical problem. Some analytical results are derived for the one-dimensional version of this model. In two dimensions, we study numerically a number of mechanical and geometrical properties for two distributions of breaking strengths and make a qualitative comparison with experimental results.