A deep learning driven uncertain full‐field homogenization method. Issue 1 (25th January 2021)

• Record Type: Journal Article
• Authors: Henkes, Alexander; Caylak, Ismail; Mahnken, Rolf
• Other Names: Kuhl D. guestEditor.; Meister A. guestEditor.; Ricoeur A. guestEditor.; Wünsch O. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 20:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202000180
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: This work is directed to uncertainty quantification of homogenized effective properties of composite materials with a complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as well as in the fiber volume fraction. They are taken into account by multivariate random variables. Uncertainty quantification is carried out by an efficient surrogate model based on pseudospectral polynomial chaos expansion and artificial neural networks, which is trained on a fast Fourier transformation based homogenization method. The numerical example deals with the comparison of the presented method to Monte Carlo‐type simulation for uncertain homogenization of spherical inclusions in a matrix material.