Two distinct length scale transition methodologies are developed to establish effective traction-separation relations for fracture in composite materials within a hierarchical multiscale framework. The two methodologies, one kinetics-based and the other kinematics-based, specify effective fracture properties that satisfy a surface-based Hill-Mandel consistency condition. Correspondingly, the total amount of energy dissipated is the same whether a crack is described in detail with micro quantities or in terms of an effective macroscopic crack. Though both methods guarantee consistency in terms of energy rates across length scales, they provide in general distinct effective traction-separation relations. Several representative samples of fiber reinforced composites are analyzed numerically, including the formation and propagation of cracks at mid-ply locations as well as (idealized) ply interfaces. Through post-processing of the microscale results, it is shown that the kinematics-based averaging method provides a macroscopic traction that is prone to rapid fluctuations while the kinetics-based averaging method shows a more smooth response but with openings that can deviate from the surface average of the microscale openings. The two methods are also compared with a previously-proposed scale transition methodology, which is a hybrid method that only satisfies the Hill-Mandel condition approximately. The suitability of the three methods is discussed in light of the results obtained from the simulations.

开发了两种不同的长度尺度转换方法，以在多层多尺度框架内为复合材料中的断裂建立有效的牵引-分离关系。两种方法，一种是基于动力学的，另一种是基于运动学的，它们指定了满足基于表面的Hill-Mandel稠度条件的有效断裂特性。相应地，无论是用微观量详细描述裂纹还是根据有效的宏观裂纹来描述，裂纹的总耗能是相同的。尽管这两种方法都保证了跨长度范围内的能量速率的一致性，但是它们通常提供了截然不同的有效牵引力-分离关系。对纤维增强复合材料的几个代表性样品进行了数值分析，包括在中层位置以及（理想化的）层界面处裂纹的形成和传播。通过对微观结果的后处理，表明基于运动学的平均方法可提供易于快速波动的宏观牵引力，而基于动力学的平均方法则显示出更平滑的响应，但开口可能会偏离表面微型开口的平均值。还将这两种方法与先前提出的比例转换方法进行了比较，后者是一种仅满足Hill-Mandel条件的混合方法。根据从仿真中获得的结果，讨论了这三种方法的适用性。结果表明，基于运动学的平均方法可提供易于快速波动的宏观牵引力，而基于动力学的平均方法则显示出更为平滑的响应，但其开孔可能会偏离微孔的表面平均值。还将这两种方法与先前提出的比例转换方法进行了比较，后者是仅能满足Hill-Mandel条件的混合方法。根据从仿真中获得的结果，讨论了这三种方法的适用性。结果表明，基于运动学的平均方法可提供易于快速波动的宏观牵引力，而基于动力学的平均方法则显示出更为平滑的响应，但其开孔可能会偏离微孔的表面平均值。还将这两种方法与先前提出的比例转换方法进行了比较，后者是一种仅满足Hill-Mandel条件的混合方法。根据从仿真中获得的结果，讨论了这三种方法的适用性。还将这两种方法与先前提出的比例转换方法进行了比较，后者是仅能满足Hill-Mandel条件的混合方法。根据从仿真中获得的结果，讨论了这三种方法的适用性。还将这两种方法与先前提出的比例转换方法进行了比较，后者是仅能满足Hill-Mandel条件的混合方法。根据从仿真中获得的结果，讨论了这三种方法的适用性。