Cohesive zone models rely on the formulation of a cohesive constitutive law. The latter describes the relation between displacement and traction in a cohesive element at an integration point. Cohesive constitutive laws in the presence of opening and shearing modes are less studied in comparison with those formulated for a single mode, particularly when the mode mixity changes. The mode mixity at an integration point is determined by the load history at the point. In this study, a formulation of the cohesive constitutive law is proposed for a mixed mode loading condition with the ability to deal with the variation in mode mixity. The proposed law is constructed incrementally and takes into account the load history. The validation is performed by simulating delamination in carbon fiber/epoxy composites in the mixed-mode bending test that is commonly used to characterize the inter-laminar fracture toughness. Although the mode mixity is fixed in this test at the specimen level, it varies locally at the element level. Cohesive constitutive laws proposed in the literature predict macroscopic delamination behavior that is dependent on the strength of the interface, while, according to the analysis of linear elastic fracture mechanics, the dependence is expected to be only on the fracture toughness. Predictions with the current formulation, where the cohesive law is updated incrementally, show low sensitivity to the interface strength. The structural response simulated with it had a good agreement with the analytical solution of linear elastic fracture mechanics.

内聚区模型依赖于内聚本构定律的制定。后者描述了在集成点上粘性元件中位移和牵引力之间的关系。与为单一模态制定的规则相比，在存在开放模态和剪切模态的情况下，对黏性本构律的研究较少，尤其是在模态混合度发生变化时。积分点的模式混合度由该点的负载历史确定。在这项研究中，针对混合模式加载条件提出了一种内聚本构关系的公式，该条件能够处理模式混合度的变化。建议的定律是逐步构造的，并考虑了载荷历史。验证是通过在通常用于表征层间断裂韧性的混合模式弯曲测试中模拟碳纤维/环氧树脂复合材料中的分层来进行的。尽管此测试中的模式混合固定在标本级别，但在元素级别局部变化。文献中提出的内聚本构定律可预测宏观剥离行为，该行为取决于界面的强度，而根据线性弹性断裂力学的分析，预计其依赖性仅取决于断裂韧性。当前公式的预测，其中内聚规律不断更新，表明对界面强度的敏感性较低。模拟的结构响应与线性弹性断裂力学的解析解具有很好的一致性。