Omnimodal topological polarization of bilayer networks: Analysis in the Maxwell limit and experiments on a 3D-printed prototype

Significance While the mechanical properties of materials are canonically dictated by their composition, in the metamaterial paradigm, structural materials are endowed with unconventional properties via the spatial arrangement and connectivity of their geometric constituents. In this vein, we introduce a family of bilayer metamaterials that display a dichotomous response to vibrations imparted on opposite edges. We prove that this edge-selectivity has topological origins, a property that ultimately grants them robustness against imperfections and disorder. We confirm our predictions on a laser-sintered prototype, whose fabrication characteristics minimize the lossiness typically associated with additive manufacturing processes. This exercise provides a proof-of-concept for the implementation of a broader class of plate-like cellular structures featuring edge-selective energy localization across a variety of modes of operation.