Phase field models have become an effective tool for predicting complex crack configurations including initiation, propagation, branching, intersecting and merging. However, several computational issues have hindered their utilisation in engineering practice, such as the convergence challenge in implicit algorithms, numerical stability issues in explicit methods and significant computational costs. Aiming to providing a more efficient numerical algorithm, this work integrates the explicit integral operator with the recently developed neighbored element method, for the first time, to solve the coupled governing equations in phase field models. In addition, the damage irreversibility can be ensured automatically, avoiding the need to introduce extra history variable for the maximum driving force in traditional algorithms. Six representative fracture benchmarks with different failure modes are simulated to verify the effectiveness of the proposed method, including the multiple cracks in heterogeneous concrete at mesoscale. It is found that this semi-explicit numerical algorithm yields consistent crack profiles and load capacities for all examples to the available experimental data and literature. In particular, the computational cost is significantly reduced when compared to the traditional explicit modelling. Therefore, the presented numerical algorithm is highly attractive and promising for phase-field simulations of complicated 3D solid fractures in structural-level engineering practices.

中文翻译：

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一种新型半显式数值算法，用于准脆性断裂的高效 3D 相场建模


相场模型已成为预测复杂裂纹形态的有效工具，包括萌生、扩展、分支、相交和合并。然而，一些计算问题阻碍了它们在工程实践中的应用，例如隐式算法中的收敛挑战、显式方法中的数值稳定性问题以及巨大的计算成本。为了提供更高效的数值算法，该工作首次将显式积分算子与最近发展的邻域元法相结合，用于求解相场模型中的耦合控制方程。此外，可以自动保证损伤的不可逆性，避免了传统算法中需要引入额外的历史变量以获得最大驱动力。对具有不同失效模式的六种代表性断裂基准进行了模拟，以验证所提方法的有效性，包括介观尺度非均质混凝土中的多重裂纹。研究发现，这种半显式数值算法对于所有示例都能产生与现有实验数据和文献一致的裂纹轮廓和负载能力。特别是，与传统的显式建模相比，计算成本显着降低。因此，所提出的数值算法对于结构级工程实践中复杂3D固体裂缝的相场模拟具有很大的吸引力和应用前景。