Transfer-learned Kolosov-Muskhelishvili Informed Neural Networks for Fracture Mechanics
This provides a unified, mesh-free, and physically consistent approach for accurate and efficient crack propagation analysis in solid mechanics, though it is incremental as it builds on existing physics-informed neural network methods.
The paper tackled the challenge of balancing governing equations and boundary conditions in physics-informed neural networks for fracture mechanics by developing a Kolosov-Muskhelishvili informed neural network with Williams enrichment, achieving average relative errors below 1% and R² above 0.99 for mode I and II loadings, and using transfer learning to integrate crack propagation criteria, reducing training time by over 70%.
Physics-informed neural networks have been widely applied to solid mechanics problems. However, balancing the governing partial differential equations and boundary conditions remains challenging, particularly in fracture mechanics, where accurate predictions strongly depend on refined sampling near crack tips. To overcome these limitations, a Kolosov-Muskhelishvili informed neural network with Williams enrichment is developed in this study. Benefiting from the holomorphic representation, the governing equations are satisfied by construction, and only boundary points are required for training. Across a series of benchmark problems, the Kolosov-Muskhelishvili informed neural network shows excellent agreement with analytical and finite element method references, achieving average relative errors below 1\% and $R^2$ above 0.99 for both mode I and mode II loadings. Furthermore, three crack propagation criteria (maximum tangential stress, maximum energy release rate, and principle of local symmetry) are integrated into the framework using a transfer learning strategy to predict crack propagation directions. The predicted paths are nearly identical across all criteria, and the transfer learning strategy reduces the required training time by more than 70\%. Overall, the developed framework provides a unified, mesh-free, and physically consistent approach for accurate and efficient crack propagation analysis.