Quasiperiodic mechanical metamaterials with extreme isotropic stiffness

Architected metamaterials are dominantly periodic, but on the other hand, natural materials usually exhibit aperiodicity or even disordered randomness. In this study, we systematically design a novel family of mechanical metamaterials that are simply composed of n+1 sets of planar plates layered in a transversely quasiperiodic manner. Through rigorous theoretical and numerical analysis, we demonstrate that these quasiperiodic metamaterials attain the extreme maximum isotropic elastic stiffness in the low density limit and can preserve over 96% optimal stiffness at moderate densities up to 50%. Moreover, we identify a dual family of quasiperiodic truss metamaterials by orientating bar members in the normal directions of aforementioned plate sets. These truss structures that are connected by construction are also stiffness optimal in the sense that they achieve the stiffness limit for truss microstructures. Both the material families possess superior directional yield strength compared to other existing periodic stiffness-optimal metamaterials. The quasiperiodic geometries offer possibilities in discovery of emerging 3D metamaterials in various areas of electromagnetics, mechanics, acoustics and others.