二维线弹性断裂分析的虚拟元方法
A Virtual Element Method for 2D linear elastic fracture analysis
AI总结：
本文提出一种虚拟元方法用于二维线弹性断裂力学中的裂纹扩展建模，通过利用虚拟元法的网格灵活性，建立基于超收敛补丁恢复的自适应网格细化策略，讨论并求解多边形网格的应力强度因子，并与传统有限元法进行对比验证。
摘要：
本文提出虚拟元方法（VEM）用于二维线弹性断裂力学（LEFM）中的裂纹扩展建模。通过利用VEM的优势，建立基于超收敛补丁恢复的自适应网格细化策略，适用于三角形、四边形及任意多边形网格。对于VEM的局部刚度矩阵，采用一种稳定的稳定化项，适用于各向同性缩放和比例。讨论并求解多边形网格的应力强度因子（SIFs）时，采用相互作用域积分法。本文提出的VEM公式通过研究其连续和不连续问题的收敛率，并与传统有限元法（FEM）的最优收敛率进行比较，最终进行了测试和验证。此外，还检查了用于有效预测非匹配元中悬挂节点存在时裂纹扩展的自适应网格细化策略。
英文摘要：
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an adaptive mesh refinement strategy based on the superconvergent patch recovery for triangular, quadrilateral as well as for arbitrary polygonal meshes. For the local stiffness matrix in VEM, we adopt a stabilization term which is stable for both isotropic scaling and ratio. Stress intensity factors (SIFs) of a polygonal mesh are discussed and solved by using the interaction domain integral. The present VEM formulations are finally tested and validated by studying its convergence rate for both continuous and discontinuous problems, and are compared with the optimal convergence rate in the conventional Finite Element Method (FEM). Furthermore, the adaptive mesh refinement strategies used to effectively predict the crack growth with the existence of hanging nodes in nonconforming elements are examined.
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