We perform a multiscale analysis for the elastic energy of a \$n\$-dimensional
bilayer thin film of thickness \$2\delta\$ whose layers are connected through an
\$\epsilon\$-periodically distributed contact zone. Describing the contact zone
as a union of \$(n-1)\$-dimensional balls of radius \$r\epsilon\$ (the holes of
the sieve) and assuming that \$\epsilon\$, we show that the asymptotic
memory of the sieve (as \$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 \$\delta\$ and \$r\$. We
also give an explicit nonlinear capacitary-type formula for the interfacial
energy density in each regime.
%0 Generic
%1 citeulike:13577512
%A Ansini, Nadia
%A Babadjian, Jean-Francois
%A Zeppieri, Caterina I.
%D 2006
%K 74q05-homogenization-in-equilibrium-problems 35b27-homogenization-equations-in-media-with-periodic-structure
%T The Neumann sieve problem and dimensional reduction: a multiscale approach
%U http://arxiv.org/abs/math/0605769
%X We perform a multiscale analysis for the elastic energy of a \$n\$-dimensional
bilayer thin film of thickness \$2\delta\$ whose layers are connected through an
\$\epsilon\$-periodically distributed contact zone. Describing the contact zone
as a union of \$(n-1)\$-dimensional balls of radius \$r\epsilon\$ (the holes of
the sieve) and assuming that \$\epsilon\$, we show that the asymptotic
memory of the sieve (as \$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 \$\delta\$ and \$r\$. We
also give an explicit nonlinear capacitary-type formula for the interfacial
energy density in each regime.
@misc{citeulike:13577512,
abstract = {{We perform a multiscale analysis for the elastic energy of a \$n\$-dimensional
bilayer thin film of thickness \$2\delta\$ whose layers are connected through an
\$\epsilon\$-periodically distributed contact zone. Describing the contact zone
as a union of \$(n-1)\$-dimensional balls of radius \$r\ll \epsilon\$ (the holes of
the sieve) and assuming that \$\delta \ll \epsilon\$, we show that the asymptotic
memory of the sieve (as \$\epsilon \to 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 \$\delta\$ 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},
archiveprefix = {arXiv},
author = {Ansini, Nadia and Babadjian, Jean-Francois and Zeppieri, Caterina I.},
biburl = {https://www.bibsonomy.org/bibtex/2e5c215efb5d29b37106976a5f453a4d8/gdmcbain},
citeulike-article-id = {13577512},
citeulike-linkout-0 = {http://arxiv.org/abs/math/0605769},
citeulike-linkout-1 = {http://arxiv.org/pdf/math/0605769},
day = 30,
eprint = {math/0605769},
interhash = {42f644173037b82ac5a7ce814c0b8259},
intrahash = {e5c215efb5d29b37106976a5f453a4d8},
keywords = {74q05-homogenization-in-equilibrium-problems 35b27-homogenization-equations-in-media-with-periodic-structure},
month = may,
posted-at = {2015-04-09 05:48:13},
priority = {2},
timestamp = {2019-04-01T03:11:24.000+0200},
title = {{The Neumann sieve problem and dimensional reduction: a multiscale approach}},
url = {http://arxiv.org/abs/math/0605769},
year = 2006
}