Maximizing the strength of fiber bundles under uniform loading

TL;DR

This paper investigates how different load redistribution schemes affect the maximum strength of fiber bundle systems under uniform loading, revealing that optimal schemes depend on the mode of loading and involve phase transitions.

Contribution

It analytically determines the maximum load capacity and optimal redistribution schemes for sudden and quasi-static loading in fiber bundle models.

Findings

Maximum strength depends on load redistribution mode.

Phase transition from partial to total failure analyzed.

Universality class varies with redistribution mechanism.

Abstract

The collective strength of a system of fibers, each having a failure threshold drawn randomly from a distribution, indicates the maximum load carrying capacity of different disordered systems ranging from disordered solids, power-grid networks, to traffic in a parallel system of roads. In many of the cases where the redistribution of load following a local failure can be controlled, it is a natural requirement to find the most efficient redistribution scheme, i.e., following which system can carry the maximum load. We address the question here and find that the answer depends on the mode of loading. We analytically find the maximum strength and corresponding redistribution schemes for sudden and quasi static loading. The associated phase transition from partial to total failure by increasing the load has been studied. The universality class is found to be dependent on the redistribution mechanism.