Multiple cracks are extremely common in aged or partially damaged concrete structures. These cracks have a decisive influence on the safety of structures. In this study, a novel multiple‐crack‐length‐controlled method is presented for analyzing the cracking behavior of multiple cracks in concrete structures. This method introduces topological variables into the finite element calculation to identify the correct crack propagation pattern of multiple‐crack problems. The values of topological variables that are used to active and inactive cracks are continually updated by the maximum stress criterion during calculation. The mathematical formulation of the proposed method is constructed in the incremental form. Thus, it is easy to be implemented in the nonlinear problems and capable of considering the influences of stress history on the plastic behaviors. Furthermore, several numerical examples with different cracking modes are studied. The results show that the proposed method provides a robust, effective, and fast way to solve the multiple‐crack problems in concrete.

中文翻译：

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混凝土结构中多个裂纹扩展的数值算法

在陈旧或部分损坏的混凝土结构中，多处裂缝极为普遍。这些裂缝对结构的安全性具有决定性的影响。在这项研究中，提出了一种新颖的多裂纹长度控制方法来分析混凝土结构中多个裂纹的开裂行为。该方法将拓扑变量引入到有限元计算中，以识别多裂纹问题的正确裂纹扩展模式。用于计算活动裂纹和非活动裂纹的拓扑变量的值会在计算过程中通过最大应力准则不断更新。所提出方法的数学公式以增量形式构建。从而，它很容易在非线性问题中实现，并且能够考虑应力历史对塑性行为的影响。此外，研究了几种具有不同裂纹模式的数值例子。结果表明，该方法为解决混凝土中的多裂纹问题提供了一种鲁棒，有效，快速的方法。