Non-Intrusive Coupling of Neural Network-Based Local Model and Explicit Dynamics Scheme: Application to Spot-Welded Plates under Impact

Solving large structural problems with multiple complex localized behaviors poses significant challenges, primarily due to the requirement of a fine mesh to capture local features and the need for a fine time step to satisfy the CFL condition. To address these difficulties, both intrusive and non-intrusive Domain Decomposition Methods (DDM) have been developed in the past, which involve solving the fine (local) and coarse (global) models separately at their respective time and space scales, with interface quantities exchanged between them. This study presents an innovative approach to further reduce computational time by replacing the Finite Element Model (FEM) at the local scale with a data-driven Reduced Order Model (ROM). The work consists of two main parts: the development of a data-driven Reduced Order Model (ROM) at the local scale, and the formulation of a non-intrusive local/global coupling [1] method to integrate the ROM with an Explicit solver. The ROM aims to establish an accurate and efficient mapping from interface velocities to interface forces, enabling the prediction of their temporal evolution. This paper proposes a modeling technique based on the Physics-Guided Architecture of Neural Networks (PGANN) [2], which incorporates physical variables beyond the input/output variables into the neural network architecture. The local/global coupling strategy relies on an iterative exchange of interface quantities between the global and local computations. An extended version, as proposed [3] for explicit dynamics problems allows the global computation to be performed only once per global time step, while multiple solutions are required for the local problems. To achieve this, we propose replacing the FEM local problem with PGANN, resulting in a significant reduction in computational time. To demonstrate the efficiency and robustness of the proposed approach, two examples will be presented: a 2D plate with a hole and a 3D case involving fast deformation of spot-welded plates. [1] L. Gendre, O. Allix, and P. Gosselet. Non-intrusive and exact global/local techniques for structural problems with local plasticity. Comput Mech., 44: 233–245 (2009). [2] J. Willard, X. Jia, S. Xu, et al. Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems. ACM Computing Surveys (2022). [3] O. Bettinotti, O. Allix, U. Perego, V. Oancea, B. Malherbe A fast weakly-intrusive multiscale method in explicit dynamics IJNME, Volume 100, Issue 8, 23: 577-595 (2014).