A Hybrid GNN-FEM Framework for Phase-Field Fracture Simulation. Physics-Preserving Hybridization for Generalizable Surrogate Modeling

2026-06-12

AI Summary

Traditional phase-field fracture simulations are computationally expensive due to the repeated solution of coupled, nonlinear, history-dependent finite element systems, limiting their applicability to complex scenarios. This work proposes a physics-preserving hybrid modeling paradigm that retains a finite element solver for displacement to ensure mechanical equilibrium and accurate boundary condition enforcement, while replacing only the phase-field update step with a graph neural network (GNN) surrogate. The incremental solution structure is preserved to faithfully capture crack evolution history. By employing dimensionless input features, a mesh-based graph representation, and a physics-informed loss function derived from the governing equations, the method demonstrates strong generalization across varying geometries, loading conditions, material properties, and discretization settings. It achieves high accuracy and robustness while significantly reducing computational cost.

Abstract

Scientific machine learning (SciML) has emerged as a promising approach for accelerating simulations of complex physical systems, yet achieving physically consistent and generalizable predictions for nonlinear, history-dependent problems remains a central challenge. In this study, we propose a hybrid GNN--FEM framework for efficient and generalizable phase-field fracture modeling. While phase-field approaches provide a robust variational framework for simulating complex crack evolution, their high computational cost limits practical applications because they require solving coupled, nonlinear, and history-dependent systems within an incremental finite element procedure. To address this challenge, a graph neural network surrogate is integrated into the conventional staggered scheme, replacing the phase-field update at each load increment while retaining the FEM-based displacement solver to enforce mechanical equilibrium and boundary conditions. By preserving the incremental solution structure, the framework remains consistent with history-dependent fracture evolution without requiring the surrogate to approximate the full solution trajectory. This selective surrogate strategy emphasizes the identification of a physically meaningful and incrementally structured learning target, rather than relying on brute-force data generation to learn the full fracture process. The proposed framework achieves strong generalization across varying geometries, loading conditions, material properties, and discretizations through dimensionless feature design, a graph-based formulation on mesh-based domains, and a physics-informed loss derived from the governing phase-field equation. Numerical experiments demonstrate that the hybrid approach reduces computational cost while maintaining accuracy compared with conventional FEM, and exhibits robust predictive performance across diverse problem settings.

Problem

• phase-field fracture
• scientific machine learning
• history-dependent problems
• generalizable surrogate modeling
• computational efficiency

Innovation

• Hybrid GNN-FEM
• Phase-field fracture
• Physics-informed surrogate
• Incremental learning
• Generalizable SciML