# Forecasting failure locations in two-dimensional disordered lattices

## TL;DR

This study uses geodesic edge betweenness centrality to predict failure points in two-dimensional disordered lattice structures, showing that failure tends to occur at edges with high betweenness, enabling failure prediction without detailed energetic analysis.

## Contribution

It introduces a network-based method using geodesic edge betweenness to forecast failure locations in disordered lattices, providing a practical diagnostic tool.

## Key findings

- Failures occur at edges with higher betweenness than the average.
- High betweenness edges are critical failure points.
- The method predicts failure locations with reasonable accuracy.

## Abstract

Forecasting fracture locations in a progressively failing disordered structure is of paramount importance when considering structural materials. We explore this issue for gradual deterioration via beam breakage of two-dimensional disordered lattices, which we represent as networks, for various values of mean degree. We study experimental samples with geometric structures that we construct based on observed contact networks in 2D granular media. We calculate geodesic edge betweenness centrality, which helps quantify which edges are on many shortest paths in a network, to forecast the failure locations. We demonstrate for the tested samples that, for a variety of failure behaviors, failures occur predominantly at locations that have larger geodesic edge betweenness values than the mean one in the structure. Because only a small fraction of edges have values above the mean, this is a relevant diagnostic to assess failure locations. Our results demonstrate that one can consider only specific parts of a system as likely failure locations and that, with reasonable success, one can assess possible failure locations of a structure without needing to study its detailed energetic states.