Inequality indices for heterogeneous systems: a tool for failure prediction
arxiv(2024)
摘要
We have numerically studied a mean-field fiber bundle model of fracture at a
non-zero temperature and acted by a constant external tensile stress. The
individual fibers fail (local damage) due to creep-like dynamics that lead up
to a catastrophic breakdown (global failure). We quantify the variations in
sizes of the resulting avalanches by calculating the Lorenz function and two
inequality indices – Gini (g) and Kolkata (k) indices – derived from the
Lorenz function. We show that the two indices cross just prior to the failure
point when the dynamics goes through intermittent avalanches. For a continuous
failure dynamics (finite numbers of fibers breaking at each time step), the
crossing does not happen. However, in that phase, the usual prediction method
i.e., linear relation between the time of minimum strain-rate and failure time,
holds. The boundary between continuous and intermittent dynamics is very close
to the boundary between crossing and non-crossing of the two indices in the
temperature-stress phase space.
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