We perform a multiscale analysis for the elastic energy of a n-dimensional bilayer thin film of thickness 2δ whose layers are connected through an ε-periodically distributed contact zone. Describing the contact zone as a union of (n - 1)-dimensional balls of radius r ? ε (the holes of the sieve) and assuming that δ ? ε, we show that the asymptotic memory of the sieve (as ε ? 0) is witnessed by the presence of an extra interfacial energy term. Moreover, we find three different limit behaviors (or regimes) depending on the mutual vanishing rate of δ and r. We also give an explicit nonlinear capacitary-type formula for the interfacial energy density in each regime.
%0 Journal Article
%1 citeulike:13577514
%A Ansini, Nadia
%A Babadjian, Jean-Francois
%A Zeppiere, Caterina I.
%D 2007
%I World Scientific Publishing Co.
%J Math. Models Methods Appl. Sci.
%K 74q05-homogenization-in-equilibrium-problems 35b27-homogenization-equations-in-media-with-periodic-structure
%N 05
%P 681--735
%R 10.1142/s0218202507002078
%T The Neumann Sieve Problem and Dimensional Reduction: A Multiscale Approach
%U http://dx.doi.org/10.1142/s0218202507002078
%V 17
%X We perform a multiscale analysis for the elastic energy of a n-dimensional bilayer thin film of thickness 2δ whose layers are connected through an ε-periodically distributed contact zone. Describing the contact zone as a union of (n - 1)-dimensional balls of radius r ? ε (the holes of the sieve) and assuming that δ ? ε, we show that the asymptotic memory of the sieve (as ε ? 0) is witnessed by the presence of an extra interfacial energy term. Moreover, we find three different limit behaviors (or regimes) depending on the mutual vanishing rate of δ and r. We also give an explicit nonlinear capacitary-type formula for the interfacial energy density in each regime.
@article{citeulike:13577514,
abstract = {{We perform a multiscale analysis for the elastic energy of a n-dimensional bilayer thin film of thickness 2δ whose layers are connected through an ε-periodically distributed contact zone. Describing the contact zone as a union of (n - 1)-dimensional balls of radius r ? ε (the holes of the sieve) and assuming that δ ? ε, we show that the asymptotic memory of the sieve (as ε ? 0) is witnessed by the presence of an extra interfacial energy term. Moreover, we find three different limit behaviors (or regimes) depending on the mutual vanishing rate of δ and r. We also give an explicit nonlinear capacitary-type formula for the interfacial energy density in each regime.}},
added-at = {2017-06-29T07:13:07.000+0200},
author = {Ansini, Nadia and Babadjian, Jean-Fran\c{c}ois and Zeppiere, Caterina I.},
biburl = {https://www.bibsonomy.org/bibtex/2d6da59b1c114badc3ca543645a97e89e/gdmcbain},
citeulike-article-id = {13577514},
citeulike-linkout-0 = {http://dx.doi.org/10.1142/s0218202507002078},
citeulike-linkout-1 = {http://www.worldscientific.com/doi/abs/10.1142/S0218202507002078},
day = 1,
doi = {10.1142/s0218202507002078},
interhash = {7700317b69b7ebeb4d6a5ae591758bc1},
intrahash = {d6da59b1c114badc3ca543645a97e89e},
journal = {Math. Models Methods Appl. Sci.},
keywords = {74q05-homogenization-in-equilibrium-problems 35b27-homogenization-equations-in-media-with-periodic-structure},
month = may,
number = 05,
pages = {681--735},
posted-at = {2015-04-09 05:49:18},
priority = {2},
publisher = {World Scientific Publishing Co.},
timestamp = {2019-04-01T03:11:24.000+0200},
title = {The {N}eumann Sieve Problem and Dimensional Reduction: A Multiscale Approach},
url = {http://dx.doi.org/10.1142/s0218202507002078},
volume = 17,
year = 2007
}