Towards understanding structure-function relationships in random fiber networks

TL;DR

This paper investigates the relationship between structure and mechanical function in random fiber networks using finite element modeling, focusing on load paths, force chains, and predicting mechanics from structural data.

Contribution

It introduces a finite element model of random fiber networks and an analytical approach to predict their mechanics based on structural information.

Findings

Identified the critical strain-stiffening transition point.

Linked force chains to shortest paths in spatial graph structures.

Provided open-source code for further research.

Abstract

Random fiber networks form the structural foundation of numerous biological tissues and engineered materials. From a mechanics perspective, understanding the structure-function relationships of random fiber networks is particularly interesting because when external force is applied to these networks, only a small subset of fibers will actually carry the majority of the load. Specifically, these load-bearing fibers propagate through the network to form load paths, also called force chains. However, the relationship between fiber network geometric structure, force chains, and the overall mechanical behavior of random fiber network structures remains poorly understood. To this end, we implement a finite element model of random fiber networks with geometrically exact beam elements, and use this model to explore random fiber network mechanical behavior. Our focus is twofold. First, we explore the mechanical behavior of single fiber chains and random fiber networks. Second, we propose and validate an interpretable analytical approach to predicting fiber network mechanics from structural information alone. Key findings include insight into the critical strain-stiffening transition point for single fiber chains and fiber networks generated from a Voronoi diagram, and a connection between force chains and the distance-weighted graph shortest paths that arise by treating fiber networks as spatial graph structures. This work marks an important step towards mapping the structure-function relationships of random fiber networks undergoing large deformations. Additionally, with our code distributed under open-source licenses, we hope that future researchers can directly build on our work to address related problems beyond the scope defined here.