Physics-informed Machine Learning and Higher-order Multi-scale Modelling of Advanced Materials in Large Structures
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This work presents a computational framework to simulate the mechanical behaviour of large structures with complex material architectures. The framework operates across two length-scales: the macroscopic scale is modelled as 5-parameter shell finite elements with first-order shear deformation, and the mesoscopic scale is modelled as solid continuum models where the local material behaviour and geometry are resolved in detail. The two length-scales are linked through a second-order computational homogenisation scheme tailored for thick shell models [1]. To replace the on-the-fly mesoscopic model analysis and homogenisation, a surrogate material model is created using a self-consistent neural network with manifold and strain energy constraints. The training data consists of strains, volume averaged stresses/moments, as well as the elastic and dissipative strain energies. During training, the model learns how the strain energy landscape varies with the loading conditions, constrained using the relationships between stresses, energies and their gradients. Based on these quantities, the constitutive tensors are inferred through automatic differentiation and learned by the model [2]. This strategy significantly reduces the computational costs to generate the material database. Furthermore, geometric deep learning is used to constrain the model outputs to a Riemannian manifold, in order to preserve the intrinsic geometry of the constitutive tensors [3]. Finally, this framework is applied to the progressive damage and nonlinear analysis of structures fabricated from composites and metamaterials. REFERENCES [1] A.K.W. Hii and B. El Said, A kinematically consistent second-order computational homogenisation framework for thick shell models, Computer Methods in Applied Mechanics and Engineering, Volume 398, 2022. [2] M. El Fallaki Idrissi, F. Praud, F. Meraghni, F. Chinesta, G.Chatzigeorgiou, Multiscale Thermodynamics-Informed Neural Networks (MuTINN) towards fast and frugal inelastic computation of woven composite structures, Journal of the Mechanics and Physics of Solids, Volume 186, 2024. [3] K. Xu, D. Z. Huang, E. Darve, Learning constitutive relations using symmetric positive definite neural networks, Journal of Computational Physics, Volume 428, 2021.
