Accurate prediction of stiffness degradation in the damaged plies (laminae) is a fundamental requirement for developing damage models for composite materials. In this study, a mesoscale analysis is proposed to predict all the effective thermo-elastic constants of damaged plies containing ply cracks and delaminations based on a numerical homogenization method. To do so, the in-plane and out-of-plane loading conditions are imposed on the three-dimensional representative volume elements (RVEs) using the periodic boundary conditions (PBCs). Considering the stress/strain fields obtained from the numerical simulations, the effective behavior of the damaged plies is evaluated. Moreover, the effects of various damage configurations, material properties, orientations of adjacent plies and ply thicknesses are studied to address the dependency of the effective elastic constants to those parameters. Numerical results reveal that the ply cracking and delaminations significantly reduce the in-plane and out-of-plane properties ($E_{22}$, $E_{33}$,$G_{12}$, $G_{13}$, $G_{23}$ and ${\nu }_{23}$) of the damaged plies. Furthermore, to demonstrate the accuracy and capability of the developed homogenization method, the homogenized properties of the damaged plies are used in the intact laminates where the stiffness of such laminates are compared with direct FE simulation and available experimental data of the laminates containing ply cracks and local delamination.

准确预测损坏层（层）中的刚度退化是开发复合材料损坏模型的基本要求。在这项研究中，提出了一种中尺度分析，以基于数值均匀化方法预测包含层裂缝和分层的损坏层的所有有效热弹性常数。为此，使用周期性边界条件 (PBC) 将平面内和平面外加载条件强加到三维代表性体积元素 (RVE) 上。考虑从数值模拟获得的应力/应变场，评估损坏层的有效行为。此外，各种损伤配置、材料特性、研究了相邻层的方向和层厚度，以解决有效弹性常数对这些参数的依赖性。数值结果表明，层板开裂和分层显着降低了面内和面外性能（${乙}_{22}$, ${乙}_{33}$,$G_{12}$, $G_{13}$, $G_{23}$ 和 ${\nu }_{23}$) 损坏的层。此外，为了证明所开发的均质化方法的准确性和能力，在完整的层压板中使用了损坏层的均质特性，其中将此类层压板的刚度与直接有限元模拟和包含层板裂纹和裂纹的层压板的可用实验数据进行了比较。局部分层。