Distribution of fracture strengths in disordered continua

Abstract

We have studied the distribution of fracture strengths in disordered continuous systems. The model that has been used is a network of nonlinear resistors which burn out and change irreversibly into insulators if their dissipated power becomes very large. Fracture occurs when a sample-spanning path of insulators is formed. The conductance of the resistors is distributed according to a probability density function (PDF). We find that if the first inverse moment of the PDF is finite, the fracture distribution is in the form of an exponential of an exponential recently derived by others, even if the system does not have the topology of a percolation cluster for which the distribution was intended. However, if the first inverse moment is infinite, neither this distribution nor the classical Weibull distribution can describe the distribution of fracture strengths, even if the system has the topology of a percolation cluster.