Abstract Fracturing two-dimensional random fiber networks of different densities (porosities) were statistically analyzed using both high-resolution finite element models and image analysis algorithms. Under small strains, the finite element fracture models revealed that networks with high relative densities were able to localize evolving fractures to small cracks while surprisingly larger cracks were required to localize fractures in networks of lower density. Further, it is indicated that the pore size distribution in fiber networks is rather diverse and can be captured using two mixed Gamma distributions; one part describing the background size distribution containing the vast majority of pores, and a second part describing the size distribution of larger pores and open regions. The second part covers less than 5% of the total network area but seems to be of paramount importance for the network’s global fracture behavior. It seems as a fiber network’s crack sensitivity is related to the average pore size in the second part of the mixed Gamma distribution. The analysis is remarkably consistent with reported experiments.

中文翻译：

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光纤网络裂纹敏感性统计分析

摘要 使用高分辨率有限元模型和图像分析算法对不同密度（孔隙率）的压裂二维随机纤维网络进行了统计分析。在小应变下，有限元断裂模型显示，具有高相对密度的网络能够将不断发展的裂缝定位到小裂缝，而令人惊讶的是，需要更大的裂缝来定位密度较低的网络中的裂缝。此外，表明纤维网络中的孔径分布相当多样化，可以使用两种混合伽马分布来捕获；一部分描述包含绝大多数孔隙的背景尺寸分布，第二部分描述较大孔隙和开放区域的尺寸分布。第二部分占网络总面积不到 5%，但似乎对网络的全局断裂行为至关重要。似乎纤维网络的裂纹敏感性与混合伽马分布的第二部分中的平均孔径有关。该分析与报告的实验非常一致。