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The author studies the elasticity and failure characteristics of a system built by 'association in parallel' of links with identical spring constant but random failure thresholds. The occurrence of the first link rupture, which is related to the theory of extreme order statistics, is contrasted with the global failure for which a central limit theorem holds. He also discusses the similarities and differences between the 'democratic' and 'hierarchical' models which differ in the mechanism by which the stress supported by links which have failed is transferred to the other stronger links. This problem gives the simplest model of elastic non-linear behaviour before global rupture occurs.
Didier Sornette (Tue,) studied this question.