Hybrid GNN-FEM Framework Accelerates Fracture Simulation

Scientific machine learning (SciML) holds immense promise for speeding up simulations of complex physical systems. However, a significant hurdle remains in achieving physically consistent and generalizable predictions, especially for nonlinear, history-dependent phenomena such as material fracture. Traditional phase-field approaches, while robust for simulating crack evolution, are computationally intensive due to their reliance on solving coupled, nonlinear systems within an incremental finite element procedure. This research introduces a hybrid GNN-FEM framework designed for efficient and generalizable phase-field fracture modeling. The core innovation lies in integrating a graph neural network surrogate to replace only the phase-field update at each load increment. Crucially, the conventional FEM-based displacement solver is retained to enforce mechanical equilibrium and boundary conditions. This selective surrogate strategy ensures that the framework remains consistent with the history-dependent nature of fracture evolution, avoiding the need for the GNN to learn the entire solution trajectory from scratch. The framework demonstrates strong generalization capabilities across varying geometries, loading conditions, material properties, and discretizations. This is achieved through dimensionless feature design, a graph-based formulation on mesh-based domains, and a physics-informed loss function derived from the governing phase-field equation. Numerical experiments confirm that this hybrid approach significantly reduces computational cost while maintaining accuracy compared to conventional FEM, offering robust predictive performance across diverse problem settings.