{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:28:48Z","timestamp":1787228928052,"version":"build-2736575974"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>The introduced notion of locally periodic two-scale convergence allows one to average a wider range of microstructures, compared to the periodic one. The compactness theorem for locally periodic two-scale convergence and the characterization of the limit for a sequence bounded in $H^1(\\Omega)$ are proven. The underlying analysis comprises the approximation of functions, with the periodicity with respect to the fast variable being dependent on the slow variable, by locally periodic functions, periodic in subdomains smaller than the considered domain but larger than the size of microscopic structures. The developed theory is applied to derive macroscopic equations for a linear elasticity problem defined in domains with plywood structures.<\/jats:p>","DOI":"10.1137\/120862338","type":"journal-article","created":{"date-parts":[[2013,1,15]],"date-time":"2013-01-15T12:50:16Z","timestamp":1358254216000},"page":"92-117","source":"Crossref","is-referenced-by-count":11,"title":["Two-Scale Convergence for Locally Periodic Microstructures and Homogenization of Plywood Structures"],"prefix":"10.1137","volume":"11","author":[{"given":"Mariya","family":"Ptashnyk","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,1,15]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500029863"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/0523084"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"G. Allaire,\n                      Shape Optimization by the Homogenization Methods\n                      , Springer, New York, 2002.","DOI":"10.1007\/978-1-4684-9286-6"},{"key":"atypb4","unstructured":"H. W. Alt,\n                      Lineare Funktionanalysis\n                      , Springer, Berlin, Heidelberg, 2002."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2004.03.006"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.3934\/nhm.2007.2.529"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02673049"},{"key":"atypb8","first-page":"19","volume":"456","author":"Bourgeat A.","year":"1994","journal-title":"J. Reine Angew. Math."},{"key":"atypb9","unstructured":"M. Briane,\n                      Homogene\u0301ne\u0301isation de mate\u0301riaux fibre\u0301s et multi-couches\n                      , Ph.D. thesis, Universite\u0301 Paris VI, Paris, 1990."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1993270607591"},{"key":"atypb11","first-page":"47","volume":"73","author":"Briane M.","year":"1994","journal-title":"J. Math. Pures Appl. (9)"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1080\/00036819908840714"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1997310505591"},{"key":"atypb14","unstructured":"J. Dixmier,\n                      Von Neumann Algebras\n                      , North-Holland, Amsterdam, 1981."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1002\/adma.200801219"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"G. P. 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Meier,\n                      Two-Scale Models of Reactive Transport in Porous Media Involving Microstructural Changes\n                      , Ph.D. thesis, University of Bremen, Bremen, Germany, 2008."},{"key":"atypb23","unstructured":"A. Muntean and T. L. van Noorden,\n                      Corrector Estimates for the Homogenization of a Locally-Periodic Medium with Areas of Low and High Diffusivity\n                      , CASA-Report 11-29, Technische Universiteit Eindhoven, Eindhoven, The Netherlands, 2011."},{"key":"atypb24","first-page":"21","author":"Murat F.","year":"1997","journal-title":"MA"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1137\/0520043"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1002\/adma.200902019"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792511000209"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160420106"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1080\/01630569408816554"},{"key":"atypb30","unstructured":"D. M. Roy and G. M. 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