In the present work, two methods, named “continuous” and “discrete”, are proposed to model the fragmentation process in brittle solids. Both methods rely on a preliminary analysis of the existing flaws population in scanned samples with X-ray micro-Computed Tomography (microCT). By converting the size of defects into critical stresses, the density of critical defects versus the applied stress level is deduced and used as an input of both a continuum and a discrete method. To do so, the concept of critical defects obscuration is implemented. Introduced in the DFH (Denoual-Forquin-Hild) micromechanics model, this concept consists in describing how cracks propagating from triggered flaws prevent neighbouring flaws from being activated. This obscuration phenomenon is implemented in the present work by using the flaws population determined via microCT analysis as an input. In the continuous method, the differential equation of the obscuration probability provided in the DFH model is integrated. In the discrete method, a cubic sub-volume of the scanned volume is considered and the growth of obscuration volumes is numerically simulated considering the real location of each critical defect and their stress of activation. Both methods provide predictions for the material dynamic strength and final cracking density according to the applied strain-rate. These two methods are applied to three types of brittle materials: an Ultra-High Performance Concrete (UHPC), a porous polycrystalline ice and a silicon carbide with spherical “fuse-flaws”. Finally, the obtained predictions are compared to the closed-form solution of the DFH model, which is based on a Weibull distribution of the critical flaws identified from bending tests. Whereas the three approaches match very well at low strain-rates, the continuous and discrete methods diverge from the DFH closed-form solution at high strain-rates, due to the activation of smaller and more numerous defects that could not be activated in the quasi-static bending tests.

在本工作中，提出了两种名为“连续”和“离散”的方法来模拟脆性固体中的破碎过程。两种方法都依赖于使用X射线计算机断层扫描（microCT）对扫描样品中现有缺陷数量进行初步分析。通过将缺陷的大小转换为临界应力，可以得出临界缺陷的密度与施加的应力水平的关系，并将其用作连续方法和离散方法的输入。为此，实施了严重缺陷掩盖的概念。在DFH（Denoual-Forquin-Hild）微力学模型中引入的这一概念在于描述从触发缺陷传播的裂纹如何阻止相邻缺陷被激活。通过使用通过microCT分析确定的缺陷数量作为输入，在本工作中实现了这种模糊现象。在连续方法中，对DFH模型中提供的遮挡概率的微分方程进行了积分。在离散方法中，考虑了扫描体积的立方子体积，并考虑了每个关键缺陷的实际位置及其激活应力，对模糊体积的增长进行了数值模拟。两种方法都可以根据所施加的应变率来预测材料的动态强度和最终的开裂密度。这两种方法适用于三种类型的脆性材料：超高性能混凝土（UHPC），多孔多晶冰和带有球形“熔断缝”的碳化硅。最后，将获得的预测结果与DFH模型的封闭形式解决方案进行比较，该模型基于弯曲测试中识别出的关键缺陷的威布尔分布。三种方法在低应变率下非常匹配，而连续和离散方法在高应变率下与DFH闭式解法有所不同，这是由于激活了较小且数量较多的缺陷，而这些缺陷在准静态下无法激活-静态弯曲测试。