Isotropic Chiral Acoustic Phonons in 3D Quasicrystalline Metamaterials

The elastic properties of three-dimensional (3D) crystalline mechanical metamaterials, unlike those of amorphous structures, are generally strongly anisotropic-even in the long-wavelength limit and for highly symmetric crystals. Aiming at isotropic linear elastic wave propagation, we therefore study 3D periodic approximants of 3D icosahedral quasicrystalline mechanical metamaterials consisting of uniaxial chiral metarods. Considering the increasing order of the approximants, we approach nearly isotropic effective speeds of sound and isotropic acoustical activity. The latter is directly connected to circularly polarized 3D metamaterial chiral acoustic phonons-for all propagation directions in three dimensions.