Towards high-accuracy axial springback: Mesh-based simulation of metal tube bending via geometry/process-integrated graph neural networks

Springback has always been a stubborn defect that affects the axial accuracy of metal bending. The finite element simulation of springback enables effective control and precise compensation to improve the forming quality. Affected by the material, size, and forming process, the generation pattern of the springback defect remains further exploration. Graph-based deep learning techniques support differentiable high-dimensional physics simulations with significantly lower computational resources and comparable accuracy. In this paper, a framework based on geometry/process-integrated Graph Neural Networks (GNN) is presented for simulating axial springback of mesh-based metal bending, with a specific focus on the tube bending. The framework adopts an encode-process-decode structure, equipped with parallel graph network blocks and data augmentation strategy, to capture the axial springback information with high fidelity in a form of mesh. Comparative experiments reveal that our framework achieves an accuracy comparable to that of finite elements method, yielding an average nodal error below 1 mm and outperforming three representative GNN baselines. The framework remarkably enhances the simulation efficiency, exhibiting a four-order-of-magnitude improvement on CPU and a six-order-of-magnitude improvement on GPU compared to finite elements method. Furthermore, we successfully apply the proposed framework to simulate the springback of plate V-bending, showcasing its robust generalization ability. These results illustrate the capability of our GNN framework to achieve the accurate and real-time springback simulation, with significant implications for digital twin development and bent tube quality optimization.