Abstract The cracking elements method (CEM) is a novel Galerkin-based numerical approach for simulating cracking and fracturing processes. It is a crack-opening approach that avoids precise descriptions of the mechanical states of crack tips and captures the initiations and propagations of multiple cracks without nodal enrichment or crack tracking. The CEM requires element types with nonlinear interpolation of the displacement field to avoid stress-locking. In the 2D condition, the 6-node triangular element (T6) and 8-node quadrilateral element (Q8) are potential candidates. However, despite the success of the formerly proposed CEM with Q8, the CEM with T6 showed considerable mesh dependencies. In this work, to solve this problem, the CEM with T6 is further investigated. The mesh dependencies are shown to be eliminated with simple modification to the real characteristic length of the T6 element in the CEM framework. Several numerical examples with regular and irregular Q8 and T6 mixed meshes are provided, indicating the effectiveness and robustness of this approach.

中文翻译：

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六节点三角形单元的开裂单元法

摘要 裂化元法（CEM）是一种新的基于伽辽金的数值方法，用于模拟裂化和压裂过程。它是一种裂纹打开方法，避免了对裂纹尖端机械状态的精确描述，并在没有节点富集或裂纹跟踪的情况下捕获多个裂纹的萌生和扩展。CEM 需要具有位移场非线性插值的单元类型以避免应力锁定。在二维条件下，6 节点三角形单元 (T6) 和 8 节点四边形单元 (Q8) 是潜在的候选对象。然而，尽管之前提出的带有 Q8 的 CEM 取得了成功，但带有 T6 的 CEM 表现出相当大的网格依赖性。在这项工作中，为了解决这个问题，进一步研究了具有 T6 的 CEM。通过对 CEM 框架中 T6 单元的真实特征长度进行简单修改，可以消除网格相关性。提供了几个具有规则和不规则 Q8 和 T6 混合网格的数值例子，表明了这种方法的有效性和鲁棒性。