Time to failure of hierarchical load-transfer models of fracture

TL;DR

This paper investigates the time to failure in hierarchical load-transfer fracture models, providing an exact computational method and showing that failure time approaches a non-zero limit as the structure height increases.

Contribution

It introduces an exact method to compute failure time for hierarchical structures and demonstrates its convergence properties for large structures under different breakdown rules.

Findings

Failure time tends to a non-zero value as structure height increases.

The method applies to both power law and exponential breakdown rules.

Provides bounds and asymptotic behavior for failure time.

Abstract

The time to failure, $T$, of dynamical models of fracture for a hierarchical load-transfer geometry is studied. Using a probabilistic strategy and juxtaposing hierarchical structures of height $n$, we devise an exact method to compute $T$, for structures of height $n+1$. Bounding $T$, for large $n$, we are able to deduce that the time to failure tends to a non-zero value when $n$ tends to infinity. This numerical conclusion is deduced for both power law and exponential breakdown rules.