A homogenization methodology for the construction of effective Cosserat substitution media for heterogeneous materials is proposed, combining a variational principle in linear elasticity with the extended Hill-Mandel lemma accounting for the introduced generalized kinematics. A general methodology is proposed which can be applied to a wide class of architected materials exhibiting such micropolar chiral effects. The tensors of effective micropolar moduli are formulated as integrals over a representative unit cell utilizing of the displacement localization operators, solution of classical and higher-order unit cell problems. The proposed method delivers size-independent higher-order effective moduli. The effective micropolar moduli of periodic lattice materials endowed with chirality and non-centrosymmetry are computed as an application of the developed homogenization method. The homogenized model is validated by comparing the local and global mechanical responses of fully resolved networks with those of plates and macrobeams architected with tetrachiral or anti-tetrachiral lattices.

提出了一种为异质材料构建有效 Cosserat 替代介质的均质化方法，将线性弹性的变分原理与扩展的 Hill-Mandel 引理相结合，解释了引入的广义运动学。提出了一种通用方法，该方法可以应用于表现出这种微极性手性效应的多种结构材料。利用位移定位算子、经典和高阶晶胞问题的解决方案，有效微极模量的张量被公式化为代表性晶胞上的积分。所提出的方法提供与尺寸无关的高阶有效模量。具有手性和非中心对称性的周期性晶格材料的有效微极模量被计算为已开发的均质化方法的应用。通过比较完全解析网络的局部和全局机械响应与使用四手性或反四手性晶格构建的板和宏梁的机械响应来验证均质模型。