Heterogeneous hydrogel fracture simulation study using community detection

This paper presents a new framework for investigating the impact of heterogeneity levels on the fracture properties of hydrogels, offering guidelines for the application of heterogeneous structure design principles. The study reveals that heterogeneous hydrogel structures generated by higher inhomogeneity levels $\beta$ exhibit increased fracture toughness compared to homogeneous ones, though excessively large $\beta$ values can diminish performance. Hydrogels with an optimal $\beta$ value of 1 statistically demonstrate superior fracture toughness. The framework integrates a multiresolution community detection algorithm, enabling the analysis of graph properties at the community scale. The findings suggest that the fracture toughness of hydrogels may be associated with a trade-off between the average community distance and the average community degree. The model successfully predicts stretch–stress curves and crack traces with high accuracy, providing a foundation for future applications such as image-based machine learning. Additionally, case studies demonstrate the adaptability of the method to multi-axial loading conditions and three-dimensional scenarios. Overall, this work provides a robust platform for advancing the understanding of hydrogels and fracture properties.