eXtended Physics Informed Neural Network Method for Fracture Mechanics Problems

Abstract

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.