Time to failure of dynamic local load-sharing fiber bundle models in 1 to 3 dimensions

Abstract Extensive Monte Carlo simulations are carried out in one, two and three dimensions for dynamic local load-sharing fiber bundle models following a power-law breaking rule with exponent ρ . This exponent controls the degree of disorder of the bundle. The results are obtained using two methods of introducing disorder in the simulations. In the standard, or classical, Monte Carlo method the disorder is quenched; in the second, or radioactive method the disorder is annealed. Both methods give identical mean time-to-failure values for systems of the same size. However, the radioactive method proves to be more efficient due to the smaller standard deviation of the probability distribution function of the time-to-failure. We take advantage of this efficiency to compute the asymptotic mean time-to-failure of large systems as a function of the degree of disorder, as parameterized by ρ . Based on these extensive simulations, conclusions are drawn regarding the upper critical dimension of time-dependent local load-sharing fiber bundle models.