Fracture strength of disordered media: Universality, interactions and tail asymptotics

TL;DR

This paper investigates the fracture strength distributions in disordered media, combining theoretical and numerical methods to understand their universality, the role of interactions, and the behavior of tail asymptotics.

Contribution

It demonstrates that the fracture strength follows the Duxbury-Leath-Beale distribution, which asymptotically approaches the Gumbel distribution, and examines the limitations of universal extreme value forms.

Findings

Fracture strength distribution is well described by the DLB distribution.

DLB distribution asymptotically flows to the Gumbel distribution.

Universal extreme value forms may not capture the non-universal low-strength tail.

Abstract

We study the asymptotic properties of fracture strength distributions of disordered elastic media by a combination of renormalization group, extreme value theory, and numerical simulation. We investigate the validity of the `weakest-link hypothesis' in the presence of realistic long-ranged interactions in the random fuse model. Numerical simulations indicate that the fracture strength is well described by the Duxbury-Leath-Beale (DLB) distribution which is shown to flow asymptotically to the Gumbel distribution. We explore the relation between the extreme value distributions and the DLB type asymptotic distributions, and show that the universal extreme value forms may not be appropriate to describe the non-universal low-strength tail.