Abstract
For years limited Monte Carlo simulations have led to the suspicion that the time to failure of hierarchically organized load-transfer models of fracture is nonzero for sets of infinite size. This fact could have profound significance in engineering practice and also in geophysics. Here, we develop an exact algebraic iterative method to compute the successive time intervals for individual breaking in systems of height in terms of the information calculated in the previous height As a byproduct of this method, rigorous lower and higher bounds for the time to failure of very large systems are easily obtained. The asymptotic behavior of the resulting lower bound leads to the evidence that the above-mentioned suspicion is actually true.
- Received 3 November 1998
DOI:https://doi.org/10.1103/PhysRevE.59.R1287
©1999 American Physical Society