A graph network-based learnable simulator for spatial-temporal prediction of rigid projectile penetration

Predicting plate penetration by rigid projectiles (PPRP) is crucial in terminal ballistics, with broad applications in civil and military engineering. Empirical and analytical methods face challenges in predicting field variables like displacement and stress in target plates. Although numerical methods offer high accuracy, they suffer from low computational efficiency. Herein, we introduce an efficient data-driven machine learning (ML) method based on graph neural networks (GNNs), named PGN, specifically tailored to address the PPRP problem. Unlike traditional ML methods that establish direct input-output mappings, PGN predicts comprehensive spatial-temporal information pertaining to the projectile-target interaction process. A thorough analysis of PGN's performance in terms of accuracy, computational efficiency and generalization ability was performed. Compared to validated results of numerical simulations, PGN maintained high precision with RMSE for displacement, stress, and strain predictions below 0.5 %, 9.5 %, and 2.1 %, respectively. It also achieved R-2 values exceeding 0.92 for the time history of projectile velocity and acceleration, while requiring only 9.8 % of the computation time compared to LS-DYNA. In generalization tests, PGN exhibited remarkable adaptability in tackling challenging scenarios that extend far beyond the training data distribution, with overall RMSE between 11 % and 13 %. Furthermore, we find that the maximum information propagation capacity of a simulated physical system must meet or exceed the information propagation need of the real-world physical phenomenon it aims to replicate. Consequently, an approach was proposed to determine the critical connectivity radius of the massage passing method directly from the wave speed in the target medium, which greatly improved the accuracy and efficiency of PGN.