The Local load sharing fiber bundle model in higher dimensions

TL;DR

This paper investigates the local load sharing fiber bundle model across dimensions one to five, revealing a transition to localization and its relation to invasion percolation, with dimensionality affecting load sharing behavior.

Contribution

It extends the fiber bundle model to higher dimensions and analyzes the transition to localization, highlighting the dimensional dependence of load sharing effects.

Findings

Transition to localized fracture depends on fiber threshold distribution.

In the localized phase, the model aligns with invasion percolation.

The difference between local and equal load sharing models diminishes with higher dimensions.

Abstract

We consider the local load sharing fiber bundle model in one to five dimensions. Depending on the breaking threshold distribution of the fibers, there is a transition where the fracture process becomes localized. In the localized phase, the model behaves as the invasion percolation model. The difference between the local load sharing fiber bundle model and the equal load sharing fiber bundle model decreases with increasing dimensionality as a power law.