用神经网络模拟多裂纹问题，精确捕捉裂纹尖端奇异性和不连续性。
eXtended Physics Informed Neural Network Method for Fracture Mechanics Problems
- 基于能量损失函数与域分解，用分层网络分别建模常规与增强解。
- 可准确模拟一维和二维复杂多裂纹，且易扩展至三维。
- 适合需要高精度裂纹模拟的工程仿真与材料力学研究者。
本文提出一种新型稳健的框架eXtended Physics-Informed Neural Network（X-PINN），用于求解含多个裂纹的断裂力学问题。通过引入基于能量的损失函数、定制化积分方案及域分解技术，结合扩展有限元法（XFEM）思想，在神经网络解空间中嵌入特殊函数，显式捕捉裂纹引起的位移不连续性与裂尖奇异行为。采用结构化设计，将标准解与增强解分别由独立神经网络建模，实现对一维与二维复杂多裂纹问题的灵活高效模拟，并具备向三维拓展的便利性。数值实验验证了该方法的有效性与鲁棒性。
原文摘要 · Abstract (English)
This paper presents eXtended Physics-Informed Neural Network (X-PINN), a novel and robust framework for addressing fracture mechanics problems involving multiple cracks in fractured media. To address this, an energy-based loss function, customized integration schemes, and domain decomposition procedures are proposed. Inspired by the Extended Finite Element Method (XFEM), the neural network solution space is enriched with specialized functions that allow crack body discontinuities and singularities at crack tips to be explicitly captured. Furthermore, a structured framework is introduced in which standard and enriched solution components are modeled using distinct neural networks, enabling flexible and effective simulations of complex multiple-crack problems in 1D and 2D domains, with convenient extensibility to 3D problems. Numerical experiments are conducted to validate the effectiveness and robustness of the proposed method.
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