Isotropic auxetic trigonal symmetry tessellations designed for FDM printing infill patterns

Mechanical metamaterials derived from Euclidean polygonal tessellations constitute a novel class of architected materials capable of exhibiting a broad spectrum of mechanical properties, including auxeticity. In this work, new monohedral and dihedral tessellations derived from a Euclidean hexagonal tessellation system possessing trigonal rotational symmetry were designed through targeted structural modifications of the original tessellation. A parametric analysis was carried out on these tessellations using finite element (FE) simulations in order to evaluate the Poisson's ratios and effective Young's moduli, followed by experimental tests on various additively-manufactured prototypes to validate the results predicted by the FE simulations. The results obtained show that these new transversely-isotropic tessellations have the capability of exhibiting the entire spectrum of two-dimensional isotropic Poisson's ratios (−1 < ν < +1) as well as a wide range of Young's moduli. The representative unit cells of these tessellations are also relatively small (compared to other irregular monohedral and dihedral networks) and highly porous, which coupled with the inherent tuneability in mechanical properties and isotropic behaviour, makes them ideal for implementation as infill patterns for Fused-Deposition Method (FDM) additively-manufactured components with low volume fractions.