A Renormalization Group Procedure for Fiber Bundle Models

TL;DR

This paper develops two renormalization group schemes for the equal load sharing fiber bundle model, conserving work and providing exact results for one version, with potential generalization to other models.

Contribution

Introduces two renormalization group methods for fiber bundle models, one exact for equal load sharing and adaptable to other models.

Findings

The first RG scheme yields exact results for equal load sharing.

The second RG scheme based on fiber location can be generalized.

Conservation of work is central to the RG approach.

Abstract

We introduce two versions of a renormalization group scheme for the equal load sharing fiber bundle model. The renormalization group is based on formulating the fiber bundle model in the language of damage mechanics. A central concept is the work performed on the fiber bundle to produce a given damage. The renormalization group conserves this work. In the first version of the renormalization group, we take advantage of ordering the strength of the individual fibers. This procedure, which is the simpler one, gives EXACT results -but cannot be generalized to other fiber bundle models such as the local load sharing one. The second renormalization group scheme based on the physical location of the individual fibers may be generalized to other fiber bundle models.