ANALYSIS OF A ONE-DIMENSIONAL FRACTURE MODEL

We investigate the dynamics of fracture of a surface layer which cover s an elastically stretched substrate. For this we map the mechanical m odel-onto its electrical counterpart, an array of resistors and fuses. We show the existence of an intrinsic correlation length which govern s the process. Starting with the investigation of the failure characte ristics of a single intact system, we obtain general expressions for t he distribution of breakup currents and for the positions of failure; these allow us to describe the fragmentation process. We show that the distribution of fragment sizes and the mean fragment sizes often scal e, and compare the analytical results to numerical simulations of the process.