Energy dissipation statistics in the random fuse model

We study the statistics of the dissipated energy in the two-dimensional random fuse model for fracture under different imposed strain conditions. By means of extensive numerical simulations we compare different ways to compute the dissipated energy. In the case of an infinitely slow driving rate (quasistatic model), we find that the probability distribution of the released energy shows two different scaling regions separated by a sharp energy crossover. At low energies, the probability of having an event of energy E decays as similar to E-1/2, which is robust and independent of the energy quantifier used (or lattice type). At high energies, fluctuations dominate the energy distribution, leading to a crossover to a different scaling regime, similar to E-2.75, whenever the released energy is computed over the whole system. On the contrary, strong finite-size effects are observed if we consider only the energy dissipated at microfractures. In a different numerical experiment, the quasistatic dynamics condition is relaxed, so that the system is driven at finite strain load rates, and we find that the energy distribution decays as P(E)similar to E-1 for all the energy range.