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.

翻译：物理知识嵌入神经网络已广泛应用于固体力学问题。然而，平衡控制偏微分方程与边界条件仍具挑战性，尤其在断裂力学中，精确预测高度依赖于裂尖附近的精细化采样。为克服这些局限，本研究提出一种融合Williams展开的Kolosov-Muskhelishvili知识嵌入神经网络。借助全纯表示，控制方程通过构造自动满足，训练仅需边界点数据。在一系列基准问题中，该网络与解析解及有限元参考结果高度吻合，在I型和II型加载条件下平均相对误差低于1%，R²值超0.99。此外，利用迁移学习策略将三种裂纹扩展准则（最大切向应力准则、最大能量释放率准则和局部对称性原理）集成至框架中，用以预测裂纹扩展方向。各准则预测的扩展路径几乎相同，且迁移学习策略减少了70%以上的训练时间。总体而言，所提出的框架提供了一种统一、无网格且物理自洽的方法，可实现精准高效的裂纹扩展分析。