Fiber bundle model under heterogeneous loading

TL;DR

This paper investigates how fiber bundle models respond to heterogeneous loading, revealing a transition from brittle to quasi-brittle failure modes and the universality of these behaviors across different threshold distributions.

Contribution

It introduces a new scheme for heterogeneous loading in fiber bundle models and analyzes its effects in both mean-field and local stress concentration limits.

Findings

Failure abruptness decreases with increasing heterogeneity.

A brittle to quasi-brittle transition occurs at a specific disorder strength.

Results are universal across different fiber strength distributions.

Abstract

The present work deals with the behavior of fiber bundle model under heterogeneous loading condition. The model is explored both in the mean-field limit as well as with local stress concentration. In the mean field limit, the failure abruptness decreases with increasing order k of heterogeneous loading. In this limit, a brittle to quasi-brittle transition is observed at a particular strength of disorder which changes with k. On the other hand, the model is hardly affected by such heterogeneity in the limit where local stress concentration plays a crucial role. The continuous limit of the heterogeneous loading is also studied and discussed in this paper. Some of the important results related to fiber bundle model are reviewed and their responses to our new scheme of heterogeneous loading are studied in details. Our findings are universal with respect to the nature of the threshold distribution adopted to assign strength to an individual fiber.