A three-dimensional analysis is presented for the prediction of the behavior of periodic fiber-reinforced composites with numerous broken fibers and debonded fiber-matrix interfaces. The locations of these defects in the composite are randomly determined. The analysis is based on the representative cell method and the higher-order theory. In the framework of the representative cell method, the problem for the representative volume element of the damaged composite that includes multiple fibers is reduced, in conjunction with the triple discrete Fourier transform, to the problem for repetitive cell of undamaged composite including just a single cell. The solution of this boundary-value problem is obtained by the higher-order theory. The inversion of the transform, in conjunction with an iterative procedure, establishes the elastic field at any point of the damaged composite. The optimal size of the representative volume element of the damaged composite within which the computations are performed is determined. The present method is capable of predicting the resulting field distributions in the composite as well as the average values of the effective moduli of the randomly damage composite and the resulting stress concentration factors. These average values and the corresponding standard deviations are determined by repeating the analysis several times (scores). A parametric study of the dependence of the effective elastic moduli and stress concentration factors upon the level of damage is performed. In addition, comparisons with a micromechanical theory predictions which are based on the analysis of a repeating unit cell, established by the assumption of spatial damage periodicity, are given.

提出了三维分析，用于预测具有大量断裂纤维和脱粘纤维-基体界面的周期性纤维增强复合材料的行为。这些缺陷在复合材料中的位置是随机确定的。该分析基于代表性细胞方法和高阶理论。在代表性单元格方法的框架中，与三重离散傅里叶变换相结合，将包含多根纤维的受损复合材料的代表性体积元素的问题减少到只包含单个单元格的未损坏复合材料的重复单元格的问题。该边值问题的解是通过高阶理论获得的。转换的倒置以及迭代过程，在损坏的复合材料的任何点建立弹性场。确定在其中执行计算的受损复合材料的代表性体积元素的最佳尺寸。本方法能够预测复合材料中的所得场分布以及随机损伤复合材料的有效模量的平均值和所得应力集中系数。这些平均值和相应的标准偏差通过重复分析几次（得分）来确定。对有效弹性模量和应力集中系数对损伤程度的依赖性进行了参数研究。另外，与基于重复晶胞分析的微机械理论预测进行比较，