Non-reciprocal three-dimensional mechanical metamaterials

Mechanical metamaterials have recently driven significant advancements, and this field has currently been extended to break the reciprocity principle in static mechanics and wave propagation. Here, we demonstrate a type of three-dimensional mechanical metamaterials that possess nonreciprocal static elastic behaviors and tunable dynamic wave properties. The metamaterial is designed with suitably tailored microstructure asymmetry, which exhibits vastly different deformation configurations upon loading from different sides. Such contrast in deformation induces distinct force–displacement responses, which gives nonlinear elastic moduli that are dependent on both the magnitude and direction of applied loads. We fabricate such metamaterials with 3D printing technique at the microscale. The non-reciprocal mechanical behavior is validated by analytical means, simulations, and experiments. Besides, tunable band structure characteristics are obtained when the metamaterial is loaded in opposite directions or by different magnitudes. The band structure deforms in asymmetrical ways, which indicates flexible control on transmit–prohibit switching of elastic waves propagation (in certain frequency ranges), and this is realized by only switching the external mechanical loading direction. These peculiar behaviors show great prospects in enabling unidirectional elasticity and wave transmission within a solid material, paving avenues to new one-way functional devices. • Three dimensional non-reciprocal metamaterials are designed. • An analytical model is developed on asymmetrical structural deformation. • The elastic moduli depend on both the magnitude and direction of applied loads. • Tunable band gap is realized by switching only the loading direction.