Identification of mechanically representative samples for aperiodic honeycombs

Honeycombs are a class of metamaterials widely used in engineering. Traditionally they have been comprised of periodic arrays of hexagonal, triangular and square cells however there have been many studies into novel variations of these lattices. Recent works have focused on the mechanical properties of metamaterials based on lattices with aperiodic order. This promising new field of study offers the potential for a wider range of available mechanical properties. With this potential comes challenges in producing, testing and simulating these structures. Analysis cannot be carried out on a unit cell as aperiodic patterns lack translational symmetry. Furthermore, it is unknown how much of the structure is required for a representative sample. This study uses a statistical approach to investigate how patch size influences the ability to accurately estimate the mechanical properties of aperiodic honeycombs. By exploiting a numerical framework requiring minimal computational resources, 1600 simulations were carried out on randomly sampled patches. This was supported by mechanically testing a targeted set of 40 additively manufactured honeycombs. It was found that in most cases increases in patch size resulted in consistent reductions in variation of properties with the samples varying by less than 5.3% from the mean when considering Young's modulus