The compression–torsion coupling metamaterials constructed by cells based on chiral mechanism of inclined rods with weak transverse constraints, display superior compression–torsion properties among the metamaterials reported previously. Aiming at metamaterials of this type, a general representative cell is extracted to reveal the relationship between the load and the deformation with considering the compression–torsion coupling effect. The stiffness matrix of the chiral 3D cell is derived based on Euler beam theory and applying dummy-load method, which is expressed as functions of the geometry parameters of cell structures and the mechanical properties of base material. The analytical predictions show good agreement with the numerical simulations. Results show that there exist optimal inclined angles of the rods corresponding to the maximal shear stiffness and the maximal compression–torsion coupling stiffness, respectively, which are both determined by the ratio of circular loop diameter to inclined rod length. This work provides guidelines for the design and analysis of compression–torsion coupling metamaterials, and opens a new avenue for theoretically analyzing the deformation coupling problem.

由具有弱横向约束的倾斜杆的手性机理构造的单元的压扭耦合超材料，在先前报道的超材料中显示出优异的压扭特性。针对这种类型的超材料，在考虑了压扭耦合效应的情况下，提取了一个具有代表性的单元，以揭示载荷与变形之间的关系。基于欧拉束理论并应用虚拟载荷方法，推导了手性3D单元的刚度矩阵，该矩阵表示为单元结构的几何参数和基础材料的力学性能的函数。分析预测与数值模拟显示出很好的一致性。结果表明，杆的最佳倾斜角分别对应于最大剪切刚度和最大压扭耦合刚度，这两者均由圆环直径与倾斜杆长度的比值决定。这项工作为压扭耦合超材料的设计和分析提供了指导，并为理论上分析变形耦合问题开辟了一条新途径。