Disordered auxetic networks with no re-entrant polygons

TL;DR

This paper demonstrates how to design disordered 2D auxetic networks with negative Poisson's ratios using convex polygons, challenging the assumption that re-entrant polygons are necessary for auxetic behavior.

Contribution

It introduces a prescriptive algorithm to create disordered auxetic networks with convex polygons and arbitrary Poisson ratios, without re-entrant polygons.

Findings

Able to achieve Poisson ratios from -1 to 1/3

Networks evolve towards isostatic point with negative Poisson ratio

Design principles applicable to 2D auxetic structures

Abstract

It is widely assumed that disordered auxetic structures (i.e. structures with a negative Poisson's ratio) must contain re-entrant polygons in $2$D and re-entrant polyhedra in $3$D. Here we show how to design disordered networks in $2$D with only convex polygons. The design principles used allow for any Poisson ratio $-1 < \nu < 1/3$ to be obtained with a prescriptive algorithm. By starting from a Delaunay triangulation with a mean coordination $<z> \simeq 6$ and $\nu \simeq 0.33$ and removing those edges that decrease the shear modulus by the least without creating any re-entrant polygons, the system evolves monotonically towards the isostatic point with $<z> \simeq 4$ and $\nu \simeq -1$.