A new deep learning framework named Crack-Net has been developed to predict crack propagation and stress–strain curves in particulate composites, as reported in a recent study published in Engineering. This innovative approach leverages artificial intelligence to address the complex problem of fracture prediction in composite materials, which are widely used in various engineering applications due to their superior mechanical properties.
The study, led by researchers from the Zhejiang Key Laboratory of Industrial Intelligence and Digital Twin, Eastern Institute of Technology, Ningbo, China, and the Department of Mechanical Engineering, Imperial College London, UK, introduces Crack-Net as a solution to the computationally expensive and time-consuming traditional finite-element methods (FEMs) used for fracture analysis. Crack-Net employs an implicit constraint technique that integrates the relationship between crack evolution and stress response into its network architecture, significantly reducing data requirements while enhancing predictive accuracy.
Crack-Net’s architecture is modeled on the U-Net, a type of convolutional neural network originally designed for medical image segmentation. This design allows Crack-Net to effectively capture spatial information and predict both the crack phase field and stress response simultaneously. The framework is trained on high-accuracy fracture development datasets obtained from phase field simulations, enabling it to handle intricate scenarios involving diverse material interfaces, varying initial conditions, and complex elastoplastic fracture processes.
The researchers conducted extensive numerical experiments to validate Crack-Net’s performance. In short-term predictions, Crack-Net demonstrated remarkable accuracy, with an R² value of 0.9993 and a mean squared error (MSE) of 0.0378 for stress predictions. The relative error of the crack phase field was found to be less than 1% for over 80% of the predictions. In long-term predictions, Crack-Net successfully predicted the entire fracture process, including the stress–strain curve and crack patterns, for various composite designs not included in the training dataset.
The study also explored Crack-Net’s capabilities in handling more complex cases, such as composites with poor interfacial adhesion and random initial cracks. The results showed that Crack-Net could accurately predict the fracture process under these challenging conditions, demonstrating its robustness and generalization ability. Furthermore, the application of transfer learning allowed Crack-Net to adapt to different material properties with minimal additional training, highlighting its potential for practical applications in material design and optimization.
In conclusion, Crack-Net represents a significant advancement in the field of computational fracture mechanics. By combining data-driven and knowledge-driven techniques, it offers a balance between computational efficiency and predictive accuracy, making it a promising tool for engineers and material scientists working with composite materials. Future work may focus on further enhancing Crack-Net’s capabilities by incorporating more explicit physical constraints and expanding its applicability to other types of composite materials and fracture scenarios.

The paper “Crack-Net: A Deep Learning Approach to Predict Crack Propagation and Stress–Strain Curves in Particulate Composites,” is authored by Hao Xu, Wei Fan, Lecheng Ruan, Rundong Shi, Ambrose C. Taylor, Dongxiao Zhang. Full text of the open access paper: https://doi.org/10.1016/j.eng.2025.02.022. For more information about Engineering, visit the website at https://www.sciencedirect.com/journal/engineering.