Metamaterials with Giant and Tailorable Nonreciprocal Elastic Moduli

Natural nonlinear materials, e.g., biological materials and polymers, are mechanically weak. It has been a major challenge to develop a nonlinear material with potential mechanical applications. Here, we develop a nonlinear elastic metamaterial with giant and tailorable-nonreciprocal elastic moduli. The metamaterial is designed with a microstructural axial asymmetry, which activated nonlinear microstructural deformations in the axial direction and microstructural residual moments. This gives a robust load dependence of the nonlinear elastic modulus (i.e., secant modulus). The nonlinear elastic modulus is observed decreasing or increasing depending on, both, the direction and magnitude of the applied load. The nonlinear elastic modulus is increased by approximately $400\mathrm{%}$ upon switching the load direction and the activation of a microstructural buckling. Thus, the nonlinear elastic modulus is generally nonreciprocal, and the metamaterial disobeys the Maxwell-Betti reciprocal theorem. This metamaterial is demonstrated by means of experimental and analytical mechanics. Various material samples are experimentally tested and their nonreciprocal elastic moduli are measured. In addition, the relation between the material's nonreciprocity and its topological mechanics is defined. The developed metamaterial can find many important mechanical applications such as making mechanical resonators with enhanced mass sensitivity.