%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 }