Comment on "Tricritical Behavior in Rupture Induced by Disorder"

TL;DR

This paper critiques a previous model of rupture in disordered media, showing that the claimed tricritical point and first-order failure are artifacts of specific assumptions, and provides a graphical method to analyze different failure behaviors.

Contribution

It demonstrates that the first-order transition in the fiber bundle model is an artifact of imposed discontinuities, and introduces a graphical approach to classify failure regimes.

Findings

First-order transition is an artifact of imposed discontinuity.

Generic physical cases do not exhibit a first-order regime.

Graphical method distinguishes different failure behaviors.

Abstract

In their letter, Andersen, Sornette, and Leung [Phys. Rev. Lett. 78, 2140 (1997)] describe possible behaviors for rupture in disordered media, based on the mean field-like democratic fiber bundle model. In this model, fibers are pulled with a force which is distributed uniformly. A fiber breaks if the stress on it exceeds a threshold chosen from a probability distribution, and the force is then redistributed over the intact fibers. Andersen et al. claim the existence of a tricritical point, separating a "first-order" regime, characterized by a sudden global failure, from a "second-order" regime, characterized by a divergence in the breaking rate. We show that a first-order transition is an artifact of a (large enough) discontinuity put by hand in the disorder distribution. Thus, in generic physical cases, a first-order regime is not present. This result is obtained from a graphical method, which, unlike Andersen at al.'s analytical solution, enables us to distinguish the various classes of qualitatively different behaviors of the model.