Based on the concept of ubiquitiform, a ubiquitiformal crack extension model is developed for quasi-brittle materials. Numerical simulations are carried out using the ABAQUS software with the XFEM-based cohesive segments method to determine the ubiquitiformal crack extension path or fracture surface profile of the material under quasi-static loading. Such a ubiquitiformal crack model removes the singularity of a fractal crack; for the latter, the boundary value problem cannot be uniquely defined. In the simulation, the material properties, e.g., the tensile strength, are assumed to obey the Weibull distribution. The meso-element equivalent method is used to determine the correlation between the Weibull distribution parameters and the aggregate gradation of concrete materials. The numerical results show that the complexities of the ubiquitiformal crack configurations are in good agreement with the previous experimental data. Through the numerical simulation, it is further demonstrated that the complexity of a ubiquitiformal crack is insensitive to the random spatial distribution of the aggregates, but more dependent on the Weibull distribution parameters which reflect the heterogeneity of the concrete.

中文翻译：

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准脆性材料的泛形裂纹扩展

基于泛在形式的概念，为准脆性材料建立了泛在形式的裂纹扩展模型。使用ABAQUS软件和基于XFEM的粘性段方法进行数值模拟，以确定准静态载荷下材料的泛形裂纹扩展路径或断裂表面轮廓。这样的泛形裂纹模型消除了分形裂纹的奇异性。对于后者，不能唯一定义边界值问题。在模拟中，假设材料特性（例如拉伸强度）服从韦布尔分布。用细观等效法确定威布尔分布参数与混凝土材料骨料级配之间的相关性。数值结果表明，普遍形裂纹构造的复杂性与先前的实验数据吻合良好。通过数值模拟，进一步证明了泛形裂纹的复杂性对骨料的随机空间分布不敏感，但更依赖于反映混凝土异质性的威布尔分布参数。