This study demonstrates a homogenization approach via a modified state-based peridynamic (PD) method to predict the effective elastic properties of composite materials with periodic microstructure. The procedure of modeling the PD unit cell (UC) of continuous fiber-reinforced composite is presented. Periodic boundary conditions are derived and implemented through the Lagrange multiplier method. A matrix-dominated approach for modeling the interphase properties between dissimilar materials is proposed. The periodicity and continuity assumptions are employed to determine the stress and strain fields, as well as the effective elastic properties. The PD-UCs of square and hexagonal packs as well as the 0/90 laminate microstructure are modeled and compared with the analytical, numerical and experimental results from the literature. Good agreement of predicted effective properties can be observed. Unlike other PD homogenization approaches, the effective material properties can be directly and individually obtained from simple loading conditions.

这项研究展示了一种通过基于状态的周向动力学（PD）改进方法的均质化方法，以预测具有周期性微结构的复合材料的有效弹性。介绍了对连续纤维增强复合材料的PD晶胞（UC）进行建模的过程。周期边界条件是通过拉​​格朗日乘数法导出并实现的。提出了一种以矩阵为主导的方法，用于对不同材料之间的相间特性进行建模。周期性和连续性假设用于确定应力场和应变场以及有效的弹性。对方形和六角形包装的PD-UC以及0/90层压板的微观结构进行了建模，并与文献中的分析，数值和实验结果进行了比较。可以观察到预测的有效特性的良好一致性。与其他PD均质化方法不同，可以从简单的加载条件直接且单独地获得有效的材料属性。