On the optimality of the window method in computational homogenization

Date
2013
Authors
Temizer, I.
Wu, T.
Wriggers, P.
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Source Title
International Journal of Engineering Science
Print ISSN
0020-7225
Electronic ISSN
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Volume
64
Issue
Pages
66 - 73
Language
English
Type
Article
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Abstract

The window method, where the microstructural sample is embedded into a frame of a homogeneous material, offers an alternative to classical boundary conditions in computational homogenization. Experience with the window method, which is essentially the self-consistent scheme but with a finite surrounding medium instead of an infinite one, indicates that it delivers faster convergence of the macroscopic response with respect to boundary conditions of pure essential or natural type as the microstructural sample size is increased to ensure statistical representativeness. In this work, the variational background for this observed optimal convergence behavior of the homogenization results with the window method is provided and the method is compared with periodic boundary conditions that it closely resembles. © 2013 Elsevier Ltd. All rights reserved.

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Keywords
Computational homogenization, Self-consistent scheme, Thermal conduction, Computational homogenization, Faster convergence, Homogeneous materials, Macroscopic response, Micro-structural, Optimal convergence, Optimality, Periodic boundary conditions, Sample sizes, Self-consistent scheme, Thermal conduction, Window methods, Boundary conditions, Optimization, Homogenization method
Citation
Published Version (Please cite this version)