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Characterising the Correlations of Failure Events: A 2‐D Block‐and‐Springs Model
Author(s) -
Ferer M.,
Smith D. H.
Publication year - 2011
Publication title -
strain
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.477
H-Index - 47
eISSN - 1475-1305
pISSN - 0039-2103
DOI - 10.1111/j.1475-1305.2010.00758.x
Subject(s) - event (particle physics) , fractal dimension , range (aeronautics) , cluster analysis , statistical physics , power law , materials science , mathematics , physics , fractal , statistics , composite material , mathematical analysis , quantum mechanics
To mimic observations from acoustic emission experiments for random systems, we used a block‐and‐springs model to investigate the effect that increasing strain has on the locations of microscopic failure events leading to macroscopic failure across the sample. Model results show that failure events, which are initially located randomly throughout the sample, begin to cluster as stress build‐up near earlier failure events. At failure, the system‐wide fracture network was found to have a fractal dimension, D f ≈ 1.29. To quantify the observed clustering, we applied a number of different measures of this space‐time behaviour: (i) the stress–strain curve; (ii) the total number of broken bonds and the average energy released by the broken bonds, (iii) the number distribution of cracks with s broken bonds, N ( s ), and the number distribution of cracks with s broken bonds or more, N (≥ s ), both of which follow power‐laws agreeing with earlier predictions; and (iv) the number–number and energy–energy correlations at time t between a failure event at position ( x ′, y ′) and a failure event at ( x ′ + x , y ′ + y ). Our results quantify the short‐range clustering, exhibiting quantitatively and qualitatively different behaviour from the long‐range clustering at failure; our results also show that the energy released outpaces the number of broken bonds.