Dilute-crack approximations for damage and fracture in disordered structures

Quenched disorder in local breaking thresholds within a two-dimensional lattice is studied, using dilute-crack approximations. Two different failure criteria are compared. Application of classical theory of strength, instead of fracture mechanics energy balance criterion, yields two times greater critical crack length, and two times greater amount of damage, in the case of failure threshold distributions without nonzero lower cutoff. Upper bounds of threshold distributions chosen correspondingly, critical voltages become similar. Normalized distribution of crack sizes appears to be independent of the applied mesoscopic failure criterion, as well as of the details of the distribution of the values for the failure threshold.