---
res:
bibo_abstract:
- 'The effective large-scale properties of materials with random heterogeneities
on a small scale are typically determined by the method of representative volumes:
a sample of the random material is chosen—the representative volume—and its effective
properties are computed by the cell formula. Intuitively, for a fixed sample size
it should be possible to increase the accuracy of the method by choosing a material
sample which captures the statistical properties of the material particularly
well; for example, for a composite material consisting of two constituents, one
would select a representative volume in which the volume fraction of the constituents
matches closely with their volume fraction in the overall material. Inspired by
similar attempts in materials science, Le Bris, Legoll and Minvielle have designed
a selection approach for representative volumes which performs remarkably well
in numerical examples of linear materials with moderate contrast. In the present
work, we provide a rigorous analysis of this selection approach for representative
volumes in the context of stochastic homogenization of linear elliptic equations.
In particular, we prove that the method essentially never performs worse than
a random selection of the material sample and may perform much better if the selection
criterion for the material samples is chosen suitably.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Julian L
foaf_name: Fischer, Julian L
foaf_surname: Fischer
foaf_workInfoHomepage: http://www.librecat.org/personId=2C12A0B0-F248-11E8-B48F-1D18A9856A87
bibo_doi: 10.1007/s00205-019-01400-w
bibo_issue: '2'
bibo_volume: 234
dct_date: 2019^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0003-9527
- http://id.crossref.org/issn/1432-0673
dct_language: eng
dct_publisher: Springer@
dct_title: The choice of representative volumes in the approximation of effective
properties of random materials@
...