Elastic Bilayer Metamaterial

Inspired by twisted bilayer graphene, we present an elastic bilayer metamaterial consisting of a plate with two graphene-like lattices of mechanical resonators on both sides of the plate. Each side can support surface resonant modes (SRM) that can interact depending on the thickness of the plate. Beyond twisting a lattice with respect to the other, the coupling strengths between the two SRM can be controlled via the plate thickness which strongly affects the dispersion of elastic waves in the bilayer structure. We theoretically characterize this dispersion by calculating the band structure for the cases of AA and AB stacking configurations, as well as for special cases of twisting angles that produces sublattices with even and odd symmetries. Furthermore, we explore the topology of the bands and uncover the possibility of creating topological elastic Valley states by breaking the symmetry of the bilayer metamaterial. The proposed bilayer plate could constitute a promising platform for manipulating mechanical waves and exploring quantum analog phenomena which could open routes toward innovative mechanical and optomechanical devices at the microscale for instance.