3D topologically polarized elastic metamaterials enable asymmetric energy isolation at finite frequencies

Topologically polarized elasticity has been extensively studied in lower dimensions, yet its three-dimensional (3D) counterpart remains largely unexplored. Here, we demonstrate omnidirectional topological elasticity in 3D structures that incorporate bending stiffness, which elevates zero-frequency topological mechanical states into finite-frequency phononic modes. These modes are localized at a single boundary, creating a pronounced stiffness contrast in both static and finite-frequency dynamic regimes. This 3D structure exhibits highly polarized mechanical behavior across all spatial dimensions, establishing omnidirectional asymmetric topological elasticity. Experimental and numerical results confirm robust, asymmetric energy isolation, arising from the interplay between bulk topological polarization and boundary-localized surface modes. Our findings establish a paradigm for 3D metamaterials, with promising applications in vibration shielding and directional wave manipulation.