Cut-Enabled Mechanical Metamaterials for Multimodal and Reprogrammable Static Nonreciprocity

Static nonreciprocity offers distinct outputs when switching the positions of action and reaction, which is of great interest for designing mechanical logic elements or soft robots. Existing mechanical metamaterials can present specific static nonreciprocal responses, but it remains challenging to obtain multiple and reprogrammable static nonreciprocal modes in a single microstructural topology. Here, a design method of cellular metamaterials is demonstrated via leaving cuts inside metacells, whose contact nonlinearity in the single metacell can offer orthogonal, uniaxial, shear (displacement and Poynting effect) static nonreciprocal modes. A framework using constitutive tensors is established to describe the multi-modal nonreciprocal behaviors. Moreover, the static nonreciprocal responses of the metamaterial array are programmable via encoding (retaining or constraining) the positions of cuts. This work offers a pathway to synthesize multiple nonreciprocal modes and control the nonreciprocal responses, enhancing the functionality of metamaterials.