A class of auxetic three-dimensional lattices

TL;DR

This paper introduces a new class of 3D lattice structures with tunable auxetic properties, capable of achieving Poisson's ratios near the stability limit and beyond, including isotropic auxetic behavior.

Contribution

It designs and characterizes a novel class of 3D auxetic lattices with controllable and extreme Poisson's ratios, including isotropic auxetic microstructures.

Findings

Microstructures can have Poisson's ratio close to -1 in all directions.

Modified microstructures can achieve Poisson's ratio below -1.

Structures can exhibit isotropic auxetic behavior.

Abstract

We propose a class of auxetic three-dimensional lattice structures. The elastic microstructure can be designed in order to have omni-directional Poisson's ratio arbitrarily close to the stability limit -1. The cubic behavior of the periodic system has been fully characterized; the minumum and maximum Poisson's ratio and the associated principal directions are given as a function of the microstructural parameters. The initial microstructure is then modified into a body centered-cubic system that can achieve a Poisson's ratio lower than -1 and that can also behave as an isotropic three-dimensional auxetic structure.