Energy dissipation statistics in the random fuse model
Abstract
We study the statistics of the dissipated energy in the twodimensional 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 ∼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, ∼E^{2.75} , whenever the released energy is computed over the whole system. On the contrary, strong finitesize 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)∼E^{1} for all the energy range.
 Publication:

Physical Review E
 Pub Date:
 April 2008
 DOI:
 10.1103/PhysRevE.77.046114
 arXiv:
 arXiv:0804.2321
 Bibcode:
 2008PhRvE..77d6114P
 Keywords:

 46.50.+a;
 62.20.M;
 Fracture mechanics fatigue and cracks;
 Structural failure of materials;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Materials Science
 EPrint:
 9 pages, ReVTeX, 8 eps figs, to appear in Phys Rev E