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Physically informed deep homogenization neural network for unidirectional multiphase/multi-inclusion thermoconductive composites

Article dans une revue avec comité de lecture
Author
JIANG, Jindong
107452 Laboratoire de Conception Fabrication Commande [LCFC]
WU, Jiajun
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
CHEN, Qiang
178323 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux [LEM3]
ccCHATZIGEORGIOU, George
178323 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux [LEM3]
ccMERAGHNI, Fodil
178323 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux [LEM3]

URI
http://hdl.handle.net/10985/23502
DOI
10.1016/j.cma.2023.115972
Date
2023-05
Journal
Computer Methods in Applied Mechanics and Engineering

Abstract

Elements of the periodic homogenization framework and deep neural network were seamlessly connected for the first time to construct a new micromechanics theory for thermoconductive composites called physically informed Deep Homogenization Network (DHN). This method utilizes a two-scale expansion of the temperature field of spatially uniform composites in terms of macroscopic and fluctuating contributions. The latter is estimated using deep neural network layers. The DHN is trained on a set of collocation points to obtain the fluctuating temperature field over the unit cell domain by minimizing a cost function given in terms of residuals of strong form steady-state heat conduction governing differential equations. Novel use of a periodic layer with several independent periodic functions with adjustable training parameters ensures that periodic boundary conditions of temperature and temperature gradients at the unit cell edges are exactly satisfied. Automatic differentiation is utilized to correctly compute the fluctuating temperature gradients. Homogenized properties and local temperature and gradient distributions of unit cells reinforced by unidirectional fiber or weakened by a hole are compared with finite-element reference results, demonstrating remarkable correlation but without discontinuities associated with temperature gradient distributions in the finite-element simulations. We also illustrate that the DHN enhanced with transfer learning provides a substantially more efficient and accurate simulation of multiple random fiber distributions relative to training the network from scratch.

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  • Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3)
  • Laboratoire de Conception Fabrication Commande (LCFC)
  • Laboratoire Procédés et Ingénierie en Mécanique et Matériaux (PIMM)

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