Bounds for the time to failure of hierarchical systems of fracture

Details Bounds for the time to failure of hierarchical systems of fracture Bounds for the time to failure of hierarchical systems of fracture

1998-11-11

arxiv.org/abs/cond-mat/9811153v3

Phys. Rev. E., 59, R1287 (1999)

Physics

Condensed Matter

Statistical Mechanics

Final version. To appear in Phys. Rev. E, Feb 1999

Scientific paper

10.1103/PhysRevE.59.R1287

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 non-zero for sets of infinite size. This fact could have a 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 $n$ in terms of the information calculated in the previous height $n-1$. 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.

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