Real-Time Simulation of Tube Hydroforming by Integrating Finite-Element Method and Machine Learning

The real-time, full-field simulation of the tube hydroforming process is crucial for deformation monitoring and the timely prediction of defects. However, this is rather difficult for finite-element simulation due to its time-consuming nature. To overcome this drawback, in this paper, a surrogate model framework was proposed by integrating the finite-element method (FEM) and machine learning (ML), in which the basic methodology involved interrupting the computational workflow of the FEM and reassembling it with ML. Specifically, the displacement field, as the primary unknown quantity to be solved using the FEM, was mapped onto the displacement boundary conditions of the tube component with ML. To this end, the titanium tube material as well as the hydroforming process was investigated, and a fairly accurate FEM model was developed based on the CPB06 yield criterion coupled with a simplified Kim-Tuan hardening model. Numerous FEM simulations were performed by varying the loading conditions to generate the training database for ML. Then, a random forest algorithm was applied and trained to develop the surrogate model, in which the grid search method was employed to obtain the optimal combination of the hyperparameters. Sequentially, the principal strain, the effective strain/stress, as well as the wall thickness was derived according to continuum mechanics theories. Although further improvements were required in certain aspects, the developed FEM-ML surrogate model delivered extraordinary accuracy and instantaneity in reproducing multi-physical fields, especially the displacement field and wall-thickness distribution, manifesting its feasibility in the real-time, full-field simulation and monitoring of deformation states.