Novel chiral honeycombs based on octahedral and dodecahedral Euclidean polygonal tessellations

Abstract

In this work, we explored the effect of ‘chiralisation’, i.e. the introduction of geometric chiral characteristics, on the mechanical properties of Euclidean polygonal tessellations containing octahedral or dodecahedral elements. This geometric transformation resulted in the design of three novel auxetic metamaterials which have the potential to exhibit large negative Poisson’s ratios (ca. −1) coupled with high levels of in-plane isotropy. We have also examined the influence of the introduction of chiral nodes on the type of geometric arrangement (i.e. whether original or dual) of the base tessellation and also show how the extent of auxeticity may be controlled by tuning the geometric parameters of these systems. This work confirms the potential of Euclidean polygonal tessellations for the design of novel auxetic metamaterials and provides new insights into the deformation mechanisms and geometric conditions which impart this anomalous property.