Mechanical couplings such as axial–shear and axial–bending have great potential in the design of active mechanical metamaterials with directional control of input and output loads in sensors and actuators. However, the current ad hoc design of mechanical coupling without theoretical support of elasticity cannot provide design guidelines for mechanical coupling with lattice geometries. Moreover, the correlation between mechanical coupling effects and geometric symmetry is not yet clearly understood. In this work, we systematically search for all possible mechanical couplings in 2D lattice structures by determining the non-zero diagonal terms in the decomposed micropolar elasticity tensor. We also correlate the mechanical couplings with the point-group symmetry of 2D lattices by applying the symmetry operation to the decomposed micropolar elasticity tensor. The decoupled micropolar constitutive equation uncovers eight coupling effects for 2D lattice structures. The symmetry operation of the decoupled micropolar elasticity tensor reveals the correlation of the mechanical coupling with the point groups. Our findings can strengthen the design of mechanical metamaterials with potential applications in areas including sensors, actuators, soft robots, and active metamaterials for elastic/acoustic wave guidance and thermal management.

轴向剪切和轴向弯曲等机械耦合在设计主动机械超材料方面具有巨大潜力，可对传感器和执行器中的输入和输出负载进行定向控制。然而，目前没有弹性理论支持的机械耦合设计无法为具有晶格几何形状的机械耦合提供设计指南。此外，机械耦合效应与几何对称性之间的相关性尚不清楚。在这项工作中，我们通过确定分解的微极弹性张量中的非零对角项系统地搜索二维晶格结构中所有可能的机械耦合。我们还通过将对称操作应用于分解的微极弹性张量，将机械耦合与二维晶格的点群对称性相关联。解耦的微极本构方程揭示了二维晶格结构的八种耦合效应。解耦的微极弹性张量的对称运算揭示了机械耦合与点群的相关性。我们的研究结果可以加强机械超材料的设计，在传感器、执行器、软机器人和用于弹性/声波引导和热管理的主动超材料等领域具有潜在应用。解耦的微极弹性张量的对称运算揭示了机械耦合与点群的相关性。我们的研究结果可以加强机械超材料的设计，在传感器、执行器、软机器人和用于弹性/声波引导和热管理的主动超材料等领域具有潜在应用。解耦的微极弹性张量的对称运算揭示了机械耦合与点群的相关性。我们的研究结果可以加强机械超材料的设计，在传感器、执行器、软机器人和用于弹性/声波引导和热管理的主动超材料等领域具有潜在应用。