The breakdown of solids under external forces is a longstanding problem, that has practical and theoretical relevance. It has been experimentally observed that the response (acoustic emission) of stressed disordered media takes place in bursts of widely distributed intensity, indicative of an internal avalanche dynamics. We have studied this problem by numerical simlations of discete lattice models and mean-field theory.
We have concentrated on disordered media and we disregard the effect thermal fluctuations. The system is driven by an increasing external load to the point of global failure. It has been experimentally observed that the response, detected by acoustic emission (AE) measurements, to an increasing external stress takes place in bursts or avalanches distributed over a wide range of scale. Examples of this are found in foam glasses fiber matrix composites, concretes, hydrogen precipitation and volcanic rocks.We have observe a similar behavior for two dimensional discrete models, such as the Random Fuse Model
We have studied the roughening of cracks in the random fuse model. This model allows to investigate the effect on the crack front roughness of the microcracks nucleating ahead of the main crack. We considered a planar crack in quasi two-dimensional geometry which applies to cases in which the material is very thin in the direction perpendicular to the crack plane. The geometry of the lattice induces a characteristic length limiting the roughness. The simulations results suggest an interpretation in terms of gradient percolation, as it is also indicated by mean-field theory.
In the case of the out of plane roughness our simulations indicate the presence of anomalous scaling in two dimensions. The (local and global) roughness exponents and the global width distributions are found to be universal with respect to the lattice geometry.
— StefanoZapperi – 10 Nov 2005