A domain decomposition-based deep finite element method for prediction of stress intensity factors

This paper proposes a domain decomposition-based deep finite element method (DD-DFEM) for prediction of stress intensity factors (SIFs) for three-dimensional cracked structures. The proposed framework synergistically combines the high-fidelity discretization philosophy of the finite element method (FEM) with the powerful approximation capability of deep neural networks. In DD-DFEM, the computational domain is decomposed along the crack surface, and two independent neural networks are employed to approximate the displacement fields on opposite sides of the crack, enabling an accurate topological representation of displacement discontinuities and crack opening behavior. Regarding the training strategy, DD-DFEM is formulated solely based on the minimization of the total potential energy (TPE) functional. Without relying on any labeled data or introducing interface coupling penalties, the dual-network system can adaptively satisfy displacement coordination and force balance conditions at subdomain interfaces while collaboratively approximating the true displacement field across the entire structure. Numerical investigations demonstrate that the proposed method can accurately reconstruct the crack-tip displacement fields under various fracture mode and yield highly accurate SIF predictions. Moreover, the training efficiency of DD-DFEM is significantly improved by incorporating pre-training, with the computation time reduced to as low as 10% of that required by the conventional finite element method. These results indicate that DD-DFEM provides an effective and efficient numerical tool for rapid fracture analysis of engineering structures.