%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 }