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.

中文翻译：

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具有巨大且可定制的不可逆弹性模量的超材料

天然非线性材料（例如生物材料和聚合物）在机械上较弱。开发具有潜在机械应用的非线性材料一直是一个重大挑战。在这里，我们开发了一种具有巨大且可定制的不可逆弹性模量的非线性弹性超材料。超材料的设计具有微结构轴向不对称性，可激活轴向上的非线性微结构变形和微结构残余力矩。这给出了非线性弹性模量（即割线模量）的稳健的载荷依赖性。观察到非线性弹性模量根据所施加载荷的方向和大小而减小或增大。非线性弹性模量大约增加$400\mathrm{％}$在切换载荷方向和激活微结构屈曲时。因此，非线性弹性模量通常是不可逆的，并且超材料不服从麦克斯韦-贝蒂互易定理。这种超材料是通过实验和分析力学来证明的。对各种材料样品进行了实验测试，并测量了它们的不可逆弹性模量。此外，还定义了材料的不可逆性与其拓扑力学之间的关系。开发的超材料可以找到许多重要的机械应用，例如制造具有增强的质量灵敏度的机械谐振器。