Effective elastic properties of novel aperiodic monotile-based lattice metamaterials

Two-dimensional aperiodic lattices emerge as remarkably isotropic metamaterials with potentially unconventional mechanical behavior. This study investigates numerically estimating the effective elastic properties, as a function of relative density, of novel two-dimensional aperiodic lattice metamaterials derived from the recently discovered aperiodic monotiles, known as the "Hat," "Turtle," and "Spectre" tiles. Furthermore, several classes of the Hat-based lattices; namely Hexagon (H), Triangle (T), Parallelogram (P), and Fan (F), are also investigated. The results show that these aperiodic lattices have isotropic elastic properties independent of relative density. The Hat-based and Turtle lattices exhibit larger elastic moduli, gradually converging to the Spectre-based lattices as relative density increases. A distinctive feature of the Hat-based lattices is their directional auxetic behaviour with an anisotropic Poisson's ratio, whereas the Turtle lattices show an auxetic behaviour only at lower relative densities. Despite anisotropic Poisson's ratios, the current aperiodic lattices maintain elastic isotropy, offering a unique blend of anisotropic auxetic behavior and isotropic elastic moduli. This study contributes to a better understanding of the elastic properties of aperiodic monotile lattice metamaterials and their potential for engineering their mechanical behavior for certain applications.