Structural Properties of Stiff Elastic Networks

TL;DR

This paper investigates the structural features of elastic beam networks that deform primarily through stretching, providing criteria to identify such networks and explaining their mechanical behavior differences.

Contribution

It introduces geometrical criteria to identify networks deforming via stretching and derives their effective elastic moduli, linking microscopic structure to macroscopic mechanics.

Findings

Identifies geometrical conditions for uniform stretching deformation.

Derives effective elastic moduli for specific network architectures.

Explains variability in mechanical responses between cellular and fiber networks.

Abstract

Networks of elastic beams can deform either by stretching or bending of their members. The primary mode of deformation (bending or stretching) crucially depends on the specific details of the network architecture. In order to shed light on the relationship between microscopic geometry and macroscopic mechanics, we characterize the structural features of networks which deform uniformly, through the stretching of the beams only. We provide a convenient set of geometrical criteria to identify such networks, and derive the values of their effective elastic moduli. The analysis of these criteria elucidates the variability of mechanical response of elastic networks. In particular, our study rationalizes the difference in mechanical behavior of cellular and fiber networks.