In materials, the evolution of crack surfaces is intimately linked with the self-contact occurring between them. The developed contact forces not only mitigate the effect of stress concentration at crack tip but also contribute significantly to the transfer of shear and normal stresses. In this article, we present a numerical framework to study the simultaneous process of fracture and self-contact between fracturing surfaces. The widely used approach, where contact constraints are enforced with the cohesive element traction separation law, is demonstrated to fail for relative displacements greater than the characteristic mesh length. A hybrid approach is proposed, which couples a node-to-segment contact algorithm with extrinsic cohesive elements. Thus, the fracture process is modeled with cohesive elements, whereas the contact and the friction constraints are enforced through a penalty-based method. This hybrid cohesive-contact approach is shown to alleviate any mesh topology limitations, making it a reliable and physically based numerical model for studying crack propagation along rough surfaces.

中文翻译：

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内聚元法与节点到段接触算法的耦合：实现与应用

在材料中，裂纹表面的演变与它们之间发生的自接触密切相关。产生的接触力不仅减轻了裂纹尖端应力集中的影响，而且对剪切应力和法向应力的传递也有显着贡献。在本文中，我们提出了一个数值框架来研究压裂面之间同时发生的断裂和自接触过程。广泛使用的方法，其中使用内聚单元牵引分离定律强制执行接触约束，被证明对于大于特征网格长度的相对位移是失败的。提出了一种混合方法，它将节点到段的接触算法与外部有凝聚力的元素。因此，断裂过程使用内聚元素建模，而接触和摩擦约束通过基于惩罚的方法强制执行。这种混合内聚接触方法被证明可以减轻任何网格拓扑限制，使其成为研究沿粗糙表面裂纹扩展的可靠且基于物理的数值模型。