Speaker
Description
Machine learning (ML) methods have been successfully applied to a broad variety of problems, such as structural engineering, elastostatics, heat transfer, fluid flow and material modelling [1-3]. A general, unified neural network approach as an ML-based counterpart of the finite element method without the need for analytic expressions for material laws is suggested [4]. The simulation process including steps from the material characterization to simulations on a structural level takes place in the proposed neural network framework. Specifically, an adaptation of the Deep Energy Method (DEM) [5] is combined with a Constitutive Artificial Neural Network (CANN) [6] and trained on measured displacement fields and prescribed boundary conditions in a coupled procedure. Tests on compressible and incompressible Neo-Hookean solids with up to twelve CANN parameters show high accuracy of the approach and very good generalization. A small extent of data is required for robust and reliable training.
[1] Le Clainche S., Ferrer E., et al. Improving aircraft performance using machine learning: Areview. Aerospace Sc \& Tech 138, 108354 (2023). https://doi.org/10.1016/j.ast.2023.108354
[2] Hildebrand, S., Klinge, S. Comparison of neural FEM and neural operator methods forapplications in solid mechanics. Neural Comput \& Applic 36, 16657–16682 (2024).
https://doi.org/10.1007/s00521-024-10132-2
[3] Hildebrand S., Klinge, S. Hybrid data-driven and physics-informed regularized learning ofcyclic plasticity with Neural Networks. Mach. Learn.: Sci. Technol. 5 045058 (2024). DOI 10.1088/2632-2153/ad95da
[4] Hildebrand S., Friedrich, J.G., Mohammadkhah, M., Klinge, S., et al. Coupled CANN-DEM Simulation in Solid Mechanics, MachineLearning: Science and Technology, 2024 (accepted)
[5] Nguyen-Tanh V.M., Zhuang X., Rabczuk T. A deep energy method for finite deformationhyperelasticity. Europ. J. Mech – A/Solids 80, 103874 (2020).
https://doi.org/10.1016/j.euromechsol.2019.103874
[6] Linka K., Hillgärtner M., et al. Constitutive artificial neural networks: A fast and generalapproach to predictive data-driven constitutive modeling by deep learning. J. Comp. Phys. 429,110010 (2021). https://doi.org/10.1016/j.jcp.2020.110010
