Extending two dimensional auxetic structures into three dimensions : the 'bolt and nut' mechanism

Abstract

Auxetic behaviour refers to the ability of material and structures to expand laterally when stretched and contract laterally when compressed. This results as a combined effect originating from the geometry of the system and the way this deforms when subjected to a load. There are various structures that deform through prescribed mechanisms that have been identified to result in auxetic behaviour. These include re-entrant and chiral honeycomb deforming through deforming through flexure [1], the rotation of rigid units in 2D and 3D (e.g. squares [2], rectangles [3], triangles [4], tetrahedral [5], etc.) as well as structures deforming through dilation-type mechanisms [6].

In this work we propose a new concept that can transform existing auxetic two dimensions lattices that involve rotation of units to three dimensional auxetics which may exhibit negative Poisson's ratios in 3D for loading in any direction.

To illustrate the proposed concept we consider a structure consisting of two parallel layers of 'rotating squares' that are attached via a "bolt" and a "nut" where the "bolt" is attached to one layer while the "nut" is attached to the other. The two layers are aligned in such a way that the square unit connected to the 'bolt' rotates in an opposite direction to the square unit attached to the "nut". When the system is uniaxially compressed in a direction in the 'rotating squares' plane, the structure will contract in this plane as a result of the 'rotating squares' mechanism. Furthermore, the "bolts" and the "nuts" will rotate in different directions in such a way that they will 'tighten up', thus decreasing the length in the third dimension.