Hierarchical auxetic and isotropic porous medium with extremely negative Poisson's ratio

TL;DR

This paper introduces a novel two-dimensional hierarchical auxetic structure with a porous medium that achieves an extremely negative Poisson's ratio close to -1, combining numerical analysis and experimental validation.

Contribution

The study presents a new hierarchical auxetic design with isotropic properties and near-minimum Poisson's ratio, validated through numerical simulations and experiments.

Findings

Poisson's ratio close to -1 achieved

Numerical and experimental validation confirms auxetic behavior

Hierarchical design enables isotropic auxetic properties

Abstract

We propose a novel two-dimensional hierarchical auxetic structure consisting of a porous medium in which a homogeneous matrix includes a rank-two set of cuts characterised by different scales. The six-fold symmetry of the perforations makes the medium isotropic in the plane. Remarkably, the mesoscale interaction between the first- and second-level cuts enables the attainment of a value of the Poisson's ratio close to the minimum reachable limit of -1. The effective properties of the hierarchical auxetic structure are determined numerically, considering both a unit cell with periodic boundary conditions and a finite structure containing a large number of repeating cells. Further, results of the numerical study are validated experimentally on a polymeric specimen with appropriately arranged rank-two cuts, tested under uniaxial tension. We envisage that the proposed hierarchical design can be useful in numerous engineering applications exploiting an extreme auxetic effect