A 2D metamaterial with auxetic out-of-plane behavior and non-auxetic in-plane behavior

TL;DR

This paper introduces a novel 2D honeycomb metamaterial that exhibits independent auxetic behaviors in in-plane and out-of-plane deformations, enabling extreme Poisson ratios through tailored lattice parameters.

Contribution

It presents a new 2D honeycomb structure with tunable auxetic properties, achieving independent in-plane and out-of-plane auxeticity, including extreme Poisson ratio values.

Findings

The structure can attain bending Poisson ratios of -1 and +1.

Continuum models accurately predict the discrete structure's behavior.

The design demonstrates independent control of in-plane and out-of-plane auxeticity.

Abstract

Customarily, in-plane auxeticity and synclastic bending behavior (i.e. out-of-plane auxeticity) are not independent, being the latter a manifestation of the former. Basically, this is a feature of three-dimensional bodies. At variance, two-dimensional bodies have more freedom to deform than three-dimensional ones. Here, we exploit this peculiarity and propose a two-dimensional honeycomb structure with out-of-plane auxetic behavior opposite to the in-plane one. With a suitable choice of the lattice constitutive parameters, in its continuum description such a structure can achieve the whole range of values for the bending Poisson coefficient, while retaining a membranal Poisson coefficient equal to 1. In particular, this structure can reach the extreme values, $-1$ and $+1$, of the bending Poisson coefficient. Analytical calculations are supported by numerical simulations, showing the accuracy of the continuum formulas in predicting the response of the discrete structure.