TY - JOUR
T1 - Machine learning aided multiscale magnetostatics
AU - Aldakheel, Fadi
AU - Soyarslan, Celal
AU - Subramani Palanisamy, Hari
AU - Elsayed, Elsayed Saber
N1 - Funding Information:
Fadi Aldakheel (FA) gratefully acknowledges support for this research by the “German Research Foundation” (DFG) in the International Research Training Group (IRTG) 2657 program (Grant Reference Number 433082294 ).
Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/9
Y1 - 2023/9
N2 - Computational material modeling using advanced numerical techniques speeds up the design process and reduces the costs of developing new engineering products. In the field of multiscale modeling, huge computation efforts are expected for modeling heterogeneous materials while trying to reach high accuracy levels. In this work, a machine learning approach, namely the convolutional neural network (CNN), is developed as a solution providing a high level of accuracy while being computationally efficient. The input for the CNN model consists of two/three-dimensional images of artificial periodic and biphasic microstructures in the form of nonoverlapping and overlapping, mono- and polydisperse circular/spherical inclusion systems, which are generated by a random sequential inhibition process. These correspond to Statistical Volume Elements (SVE). Considering linear magnetostatics at the microscale, the output is the apparent permeability of the SVE. Training and testing data for the apparent properties is produced with finite element method-based two-scale asymptotic homogenization. The model efficiency is revealed by employing some representative examples in two and three-dimensional settings. In this regard, the performance of the CNN model is assessed with the applied computational homogenization method relating to the accuracy and computational efficiency. The results with the CNN model show high accuracy in predicting the homogenized permeability and a significant decrease in computation time.
AB - Computational material modeling using advanced numerical techniques speeds up the design process and reduces the costs of developing new engineering products. In the field of multiscale modeling, huge computation efforts are expected for modeling heterogeneous materials while trying to reach high accuracy levels. In this work, a machine learning approach, namely the convolutional neural network (CNN), is developed as a solution providing a high level of accuracy while being computationally efficient. The input for the CNN model consists of two/three-dimensional images of artificial periodic and biphasic microstructures in the form of nonoverlapping and overlapping, mono- and polydisperse circular/spherical inclusion systems, which are generated by a random sequential inhibition process. These correspond to Statistical Volume Elements (SVE). Considering linear magnetostatics at the microscale, the output is the apparent permeability of the SVE. Training and testing data for the apparent properties is produced with finite element method-based two-scale asymptotic homogenization. The model efficiency is revealed by employing some representative examples in two and three-dimensional settings. In this regard, the performance of the CNN model is assessed with the applied computational homogenization method relating to the accuracy and computational efficiency. The results with the CNN model show high accuracy in predicting the homogenized permeability and a significant decrease in computation time.
KW - Convolutional Neural Network (CNN)
KW - Homogenization
KW - Magnetostatics
KW - 2023 OA procedure
UR - http://www.scopus.com/inward/record.url?scp=85166626338&partnerID=8YFLogxK
U2 - 10.1016/j.mechmat.2023.104726
DO - 10.1016/j.mechmat.2023.104726
M3 - Article
AN - SCOPUS:85166626338
SN - 0167-6636
VL - 184
JO - Mechanics of materials
JF - Mechanics of materials
M1 - 104726
ER -