Abstract All crack models developed to date can be classified into discrete- and continuum-based approaches. While discrete models are advantageously capable of capturing the kinetics of fractures, continuum-based approaches still pique considerable interest due to their straightforward implementation within the finite element method (FEM) framework. The cracking element method (CEM), a recently developed numerical approach for simulating quasi-brittle fracturing, is based on the FEM and does not need remeshing, a nodal cover algorithm, nodal enrichment or a crack-tracking strategy. The CEM takes self-propagating disconnected cracking segments to represent crack paths and naturally captures crack initiation and propagation processes. However, as with other types of continuum-based approaches that employ discontinuous crack paths, one critical question remains: Can the crack openings can be reliably and accurately obtained? To answer this question, a detailed study on the released energy, kinetic model, and displacement between the upper and lower facets of a crack is required. Multiple tests are conducted in this paper, and the results of the CEM are compared with those of the interface element method (IEM), which explicitly describes the crack openings. For reference and comparison purposes, an a priori crack path obtained by using an equivalent crack path (cracked elements) previously obtained from the CEM is implemented for the IEM. The crack openings obtained by the CEM and IEM are subsequently compared, and the results indicate that the crack openings and dissipated energy obtained by the CEM generally agree well with those obtained by the IEM. These findings highlight the effectiveness of utilizing disconnected cracking segments and further demonstrate the robustness and reliability of the CEM.

中文翻译：

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基于连续介质的不连续裂纹模型中的裂纹张开和能量耗散

摘要 迄今为止开发的所有裂纹模型都可以分为基于离散和连续的方法。虽然离散模型能够有利地捕捉裂缝动力学，但基于连续介质的方法仍然引起了相当大的兴趣，因为它们在有限元方法 (FEM) 框架内的直接实现。裂纹元法 (CEM) 是一种最近开发的模拟准脆性压裂的数值方法，它基于有限元法，不需要重新网格划分、节点覆盖算法、节点富集或裂纹跟踪策略。CEM 采用自传播的不连续裂纹段来表示裂纹路径，并自然地捕捉裂纹萌生和扩展过程。然而，与采用不连续裂纹路径的其他类型的基于连续体的方法一样，一个关键问题仍然存在：能否可靠准确地获取裂纹开口？要回答这个问题，需要对裂纹的上下端面之间的释放能量、动力学模型和位移进行详细研究。本文进行了多次测试，并将 CEM 的结果与明确描述裂纹开口的界面元方法 (IEM) 的结果进行了比较。为了参考和比较，IEM 实现了使用先前从 CEM 获得的等效裂纹路径（裂纹元素）获得的先验裂纹路径。随后比较了 CEM 和 IEM 获得的裂纹开口，结果表明 CEM 获得的裂纹开口和耗散能量与 IEM 获得的裂纹开口和耗散能量基本一致。