"Forecasting Failure Locations in 2-Dimensional Disordered Lattices"

One of my papers (which we published in PNAS) now has its final coordinates (volume, page numbers, etc.), after previously being posted in 'advanced access'. Here are some details about the article.

Title: Forecasting Failure Locations in 2-Dimensional Disordered Lattices

Authors: Estelle Berthier, Mason A. Porter, and Karen E. Daniels

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 2-dimensional (2D) 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.

Significance Statement: Disordered lattices are used widely for mechanical applications because they are lightweight and robust. Due to their heterogeneous structure, it is a complicated task to understand and forecast their progressive degradation. To safely use these materials and design structures with optimized mechanical properties, it is crucial to understand where failures occur. We show that a simple test that consists of comparing the importance of a beam with respect to the other beams in a lattice permits a successful forecast of the locations of failures. It allows one to consider only a small fraction of the beams as likely failure locations. Our approach also provides a roadmap for studies of failures in other spatial networks.