Engineering zero modes in transformable mechanical metamaterials

In the field of flexible metamaterial design, harnessing zero modes plays a key part in enabling reconfigurable elastic properties of the metamaterial with unconventional characteristics. However, only quantitative enhancement of certain properties succeeds in most cases rather than qualitative transformation of the metamaterials' states or/and functionalities, due to the lack of systematic designs on the corresponding zero modes. Here, we propose a 3D metamaterial with engineered zero modes, and experimentally demonstrate its transformable static and dynamic properties. All seven types of extremal metamaterials ranging from null-mode (solid state) to hexa-mode (near-gaseous state) are reported to be reversibly transformed from one state to another, which is verified by the 3D-printed Thermoplastic Polyurethanes prototypes. Tunable wave manipulations are further investigated in 1D-, 2D- and 3D-systems. Our work sheds lights on the design of flexible mechanical metamaterials, which can be potentially extended from the mechanical to the electro-magnetite, the thermal or other types.