Following the so-called Cracking Elements Method (CEM), recently presented in \cite{Yiming:14,Yiming:16}, we propose a novel Galerkin-based numerical approach for simulating quasi-brittle fracture, named Global Cracking Elements Method (GCEM). For this purpose the formulation of the original CEM is reorganized. The new approach is embedded in the standard framework of the Galerkin-based Finite Element Method (FEM), which uses disconnected element-wise crack openings for capturing crack initiation and propagation. The similarity between the proposed Global Cracking Elements (GCE) and the standard 9-node quadrilateral element (Q9) suggests a special procedure: the degrees of freedom of the center node of the Q9, originally defining the displacements, are "borrowed" to describe the crack openings of the GCE. The proposed approach does not need remeshing, enrichment, or a crack-tracking strategy, and it avoids a precise description of the crack tip. Several benchmark tests provide evidence that the new approach inherits from the CEM most of the advantages. The numerical stability and robustness of the GCEM are better than the ones of the CEM. However, presently only quadrilateral elements with nonlinear interpolations of the displacement field can be used.

中文翻译：

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全局裂纹元素：一种基于伽辽金方法模拟准脆性断裂的新工具

继最近在 \cite{Yiming:14,Yiming:16} 中提出的所谓的裂纹单元法（CEM）之后，我们提出了一种新的基于伽辽金的数值方法来模拟准脆性断裂，称为全局裂纹单元法（GCEM） ）。为此，重新组织了原始 CEM 的公式。新方法嵌入在基于伽辽金的有限元方法 (FEM) 的标准框架中，该方法使用不连续的元素级裂纹开口来捕获裂纹的萌生和扩展。提议的全局裂纹单元 (GCE) 和标准 9 节点四边形单元 (Q9) 之间的相似性表明了一个特殊的程序：Q9 中心节点的自由度，最初定义了位移，被“借用”来描述GCE的裂缝开口。所提出的方法不需要重新网格划分、富集或裂纹跟踪策略，并且避免了对裂纹尖端的精确描述。多项基准测试提供证据表明，新方法继承了 CEM 的大部分优势。GCEM 的数值稳定性和鲁棒性优于 CEM。然而，目前只能使用具有位移场非线性插值的四边形单元。