Effect of localized loading on failure threshold of fiber bundles

TL;DR

This paper studies how localized initial loading affects the failure threshold of fiber bundle systems, revealing non-monotonic behavior and a critical initial load fraction that maximizes damage, with implications for system stability.

Contribution

It uncovers the non-monotonic relationship between initial load fraction and failure threshold in fiber bundles, highlighting a crossover behavior dependent on load sharing range.

Findings

Failure threshold varies non-monotonically with initial load fraction.

Existence of a finite initial load fraction that maximizes damage.

Crossover behavior observed in 1D and 2D models.

Abstract

We investigate the global failure threshold of an interconnected set of elements, when a finite fraction of the elements initially share an externally applied load. The study is done under the framework of random fiber bundle model, where the fibers are linear elastic objects attached between two plates. The failure threshold of the system varies non-monotonically with the fraction of the system on which the load is applied initially, provided the load sharing mechanism following a local failure is sufficiently wide. In this case, there exists a finite value for the initial loading fraction, for which the damage on the system will be maximum, or in other words the global failure threshold will be minimum for a finite value of the initial loading fraction. This particular value of initial loading fraction, however, goes to zero when the load sharing is sufficiently local. Such crossover behavior, seen for both one and two dimensional versions of the model, can give very useful information about stability of interconnected systems with random failure thresholds.