Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395, Mager, Lucas and Rege, Ameya ORCID: 0000-0001-9564-5482 (2025). Computational homogenization for aerogel-like polydisperse open-porous materials using neural network-based surrogate models on the microscale. Computational Mechanics. pp. 1-21. Springer Nature. ISSN 0178-7675

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Abstract

The morphology of nanostructured materials exhibiting a polydisperse porous space, such as aerogels, is very open porous and fine grained. Therefore, a simulation of the deformation of a large aerogel structure resolving the nanostructure would be extremely expensive. Thus, multi-scale or homogenization approaches have to be considered. Here, a computational scale bridging approach based on the FE 2 method is suggested, where the macroscopic scale is discretized using finite elements while the microstructure of the open-porous material is resolved as a network of Euler–Bernoulli beams. Here, the beam frame based RVEs (representative volume elements) have pores whose size distribution follows the measured values for a specific material. This is a well-known approach to model aerogel structures. For the computational homogenization, an approach to average the first Piola–Kirchhoff stresses in a beam frame by neglecting rotational moments is suggested. To further overcome the computationally most expensive part in the homogenization method, that is, solving the RVEs and averaging their stress fields, a surrogate model is introduced based on neural networks. The network’s input is the localized deformation gradient on the macroscopic scale and its output is the averaged stress for the specific material. It is trained on data generated by the beam frame based approach. The effiency and robustness of both homogenization approaches is shown numerically, the approximation properties of the surrogate model is verified for different macroscopic problems and discretizations. Different (Quasi-)Newton solvers are considered on the macroscopic scale and compared with respect to their convergence properties.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel UNSPECIFIED https://orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin UNSPECIFIED https://orcid.org/0000-0002-4232-9395 UNSPECIFIED Mager, Lucas UNSPECIFIED UNSPECIFIED UNSPECIFIED Rege, Ameya UNSPECIFIED https://orcid.org/0000-0001-9564-5482 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-797055
Identification Number:	10.1007/s00466-024-02588-9
Journal or Publication Title:	Computational Mechanics
Page Range:	pp. 1-21
Date:	1 February 2025
Publisher:	Springer Nature
ISSN:	0178-7675
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Mathematics
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/79705