Abstract This paper introduces a new extended Voronoi cell finite-element method (X-VCFEM) for modelling the propagation of multiple cracks in brittle materials. The direction of the crack propagation is adaptively determined in terms of the maximum energy release rate near the crack tip, and we apply a remeshing strategy that a node at a last incremental crack tip in the crack advance process is replaced by a node pairs to realize the gradual crack propagation. In order to accurately capture crack-tip stress concentrations, some singular stress terms of Williams expansion in the vicinity of crack tips are introduced in the assumed stress hybrid formulation which also includes the polynomial terms and the reciprocal terms. Then several numerical examples are used to demonstrate the effectiveness and accuracy of X-VCFEM enriched by some singular stress terms of Williams expansion by comparing X-VCFEM results with those computed by the commercial finite element package ABAQUS or established results in the literature. At last, two numerical examples are given to simulate multiple crack propagation in brittle media. The effects of morphological distributions such as length, orientation and dispersion on the crack propagation are studied. It is obvious that the X-VCFEM has great advantage of analyzing large regions of the microstructure with multiple growing and interacting cracks.

中文翻译：

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脆性材料中多裂纹扩展的扩展 Voronoi 单元有限元方法

摘要 本文介绍了一种新的扩展 Voronoi 单元有限元方法 (X-VCFEM)，用于模拟脆性材料中多裂纹的扩展。根据裂纹尖端附近的最大能量释放率自适应地确定裂纹扩展的方向，我们应用重新网格化策略，将裂纹推进过程中最后一个增量裂纹尖端的节点替换为节点对来实现裂纹逐渐扩展。为了准确捕获裂纹尖端应力集中，在假设应力混合公式中引入了裂纹尖端附近威廉姆斯膨胀的一些奇异应力项，其中还包括多项式项和倒数项。然后，通过将 X-VCFEM 结果与商业有限元软件包 ABAQUS 计算的结果或文献中的既定结果进行比较，使用几个数值例子来证明通过威廉斯展开的一些奇异应力项丰富的 X-VCFEM 的有效性和准确性。最后给出了两个数值算例来模拟脆性介质中的多裂纹扩展。研究了形态分布如长度、取向和分散对裂纹扩展的影响。很明显，X-VCFEM 在分析具有多个生长和相互作用裂纹的大面积显微组织方面具有很大的优势。给出了两个数值例子来模拟脆性介质中的多裂纹扩展。研究了形态分布如长度、取向和分散对裂纹扩展的影响。很明显，X-VCFEM 在分析具有多个生长和相互作用裂纹的大面积显微组织方面具有很大的优势。给出了两个数值例子来模拟脆性介质中的多裂纹扩展。研究了形态分布如长度、取向和分散对裂纹扩展的影响。很明显，X-VCFEM 在分析具有多个生长和相互作用裂纹的大面积显微组织方面具有很大的优势。