Analysis of a one-dimensional fracture model

The authors investigate the dynamics of fracture of a surface layer which covers an elastically stretched substrate. For this they map the mechanical model onto its electrical counterpart, an array of resistors and fuses. They show the existence of an intrinsic correlation length which governs the process. Starting with the investigation of the failure characteristics of a single intact system, they obtain general expressions for the distribution of breakup currents and for the positions of failure; these allow them to describe the fragmentation process. They show that the distribution of fragment sizes and the mean fragment sizes often scale, and compare the analytical results to numerical simulations of the process.