A comprehensive strategy for the simulation of mixed-mode cohesive crack propagation in a mesh of originally self-stabilized Virtual Elements (VEs) is proposed. Exploiting the VEs substantial insensitivity to mesh distortion, the propagating cohesive crack is accommodated within existing self-stabilized first-order quadrilateral VEs by simply adding new edges separated by a cohesive interface. The added edges make however the VE unstable and a new procedure for the stabilization of initially stable VE is developed. The method is formulated within a recently proposed Hu–Washizu variational framework, allowing for a higher order, independent modeling of stresses. In this way, a more accurate estimate of the stress at the tip of the cohesive process zone can be achieved allowing for a more accurate assessment of crack propagation conditions and direction. The proposed method is validated by application to several benchmark problems.

中文翻译：

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各向同性弹性固体中 2D 混合模式内聚裂纹扩展的自稳定虚拟单元建模


该文提出了一种模拟混合模式内聚裂纹在原始自稳性虚拟单元 （VEs） 网格中扩展的综合策略。利用 VE 对网格变形的极不敏感性，通过简单地添加由内聚界面分隔的新边缘，将传播的内聚裂纹容纳在现有的自稳定一阶四边形 VE 中。然而，添加的边缘使 VE 不稳定，并开发了一种稳定初始稳定 VE 的新程序。该方法是在最近提出的 胡-Washizu 变分框架中制定的，允许对应力进行更高阶的独立建模。通过这种方式，可以更准确地估计内聚工艺区尖端的应力，从而更准确地评估裂纹扩展条件和方向。所提出的方法通过应用于几个基准问题进行了验证。