Auxetic two-dimensional lattice with Poisson's Ratio arbitrarily close to -1

TL;DR

This paper introduces a novel 2D lattice structure capable of achieving a Poisson's ratio arbitrarily close to -1, supported by experimental validation and analytical modeling of its effective properties.

Contribution

The study presents a new lattice design with tunable Poisson's ratio near -1, including experimental testing and full analytical expressions for its macroscopic properties.

Findings

Experimental uniaxial tests confirm the negative Poisson's ratio close to -1.

Analytical models accurately predict the effective properties based on microstructure.

Different micro-geometries lead to isotropic or cubic symmetry behaviors.

Abstract

In this paper we propose a new lattice structure having macroscopic Poisson's ratio arbitrarily close to the stability limit -1. We tested experimentally the effective Poisson's ratio of the micro-structured medium; the uniaxial test has been performed on a thermoplastic lattice produced with a 3d printing technology. A theoretical analysis of the effective properties has been performed and the expression of the macroscopic constitutive properties is given in full analytical form as a function of the constitutive properties of the elements of the lattice and on the geometry of the microstructure. The analysis has been performed on three micro-geometry leading to an isotropic behaviour for the cases of three-fold and six-fold symmetry and to a cubic behaviour for the case of four-fold symmetry.