{"id":"https://openalex.org/W1997914848","doi":"https://doi.org/10.1137/070705714","title":"Homogenization of Elastic Media with Gaseous Inclusions","display_name":"Homogenization of Elastic Media with Gaseous Inclusions","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1997914848","doi":"https://doi.org/10.1137/070705714","mag":"1997914848"},"language":"en","primary_location":{"id":"doi:10.1137/070705714","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070705714","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00180307","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069228976","display_name":"L. Baffico","orcid":"https://orcid.org/0000-0001-7050-0906"},"institutions":[{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I4387155825","display_name":"Laboratoire de Math\u00e9matiques Nicolas Oresme","ror":"https://ror.org/03jm2hc44","country_code":null,"type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210105918","https://openalex.org/I4387155825","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"L. Baffico","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Nicolas Oresme"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Nicolas Oresme","institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I4387155825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079231074","display_name":"C\u00e9line Grandmont","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. Grandmont","raw_affiliation_strings":["Numerical simulation of biological flows"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Numerical simulation of biological flows","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089357934","display_name":"Yvon Maday","orcid":"https://orcid.org/0000-0002-0443-6544"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Y. Maday","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072338061","display_name":"Axel Osses","orcid":"https://orcid.org/0000-0001-6833-4064"},"institutions":[{"id":"https://openalex.org/I124618812","display_name":"Mathematics Research Center","ror":"https://ror.org/02nhmp827","country_code":"MX","type":"facility","lineage":["https://openalex.org/I124618812"]},{"id":"https://openalex.org/I4387155550","display_name":"Center for Mathematical Modeling","ror":"https://ror.org/00wz2vk41","country_code":"CL","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4387155550","https://openalex.org/I69737025"]}],"countries":["CL","MX"],"is_corresponding":false,"raw_author_name":"A. Osses","raw_affiliation_strings":["Centro de Modelamiento Matem\u00e1tico [Santiago]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Modelamiento Matem\u00e1tico [Santiago]","institution_ids":["https://openalex.org/I124618812","https://openalex.org/I4387155550"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8279,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.74509672,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"7","issue":"1","first_page":"432","last_page":"465"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.9114023447036743},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.7767252922058105},{"id":"https://openalex.org/keywords/linear-elasticity","display_name":"Linear elasticity","score":0.6618065237998962},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.5898240804672241},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5795486569404602},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5050154328346252},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4802406430244446},{"id":"https://openalex.org/keywords/asymptotic-homogenization","display_name":"Asymptotic homogenization","score":0.47986263036727905},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.4540073573589325},{"id":"https://openalex.org/keywords/nonlinear-elasticity","display_name":"Nonlinear elasticity","score":0.4323920011520386},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.365911066532135},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3499929904937744},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.2710975408554077},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.16647547483444214},{"id":"https://openalex.org/keywords/composite-number","display_name":"Composite number","score":0.12064293026924133},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.08400866389274597}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.9114023447036743},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.7767252922058105},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.6618065237998962},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.5898240804672241},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5795486569404602},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5050154328346252},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4802406430244446},{"id":"https://openalex.org/C2777581374","wikidata":"https://www.wikidata.org/wiki/Q4812185","display_name":"Asymptotic homogenization","level":3,"score":0.47986263036727905},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.4540073573589325},{"id":"https://openalex.org/C2983365874","wikidata":"https://www.wikidata.org/wiki/Q193514","display_name":"Nonlinear elasticity","level":3,"score":0.4323920011520386},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.365911066532135},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3499929904937744},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2710975408554077},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.16647547483444214},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.12064293026924133},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08400866389274597},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/070705714","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070705714","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.232.6500","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.232.6500","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/18/03/07/PDF/bagrmaos_preprint.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00180307v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00180307","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2008, 7 (1), pp.33","raw_type":"Journal articles"},{"id":"pmh:oai:americanae.aecid.es:3228715","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3228715","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MULTISCALE MODELING & SIMULATION (PRINT)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/177178","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/177178","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MULTISCALE MODELING & SIMULATION (PRINT)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repositorio.uchile.cl:2250/125055","is_oa":false,"landing_page_url":"http://repositorio.uchile.cl/handle/2250/125055","pdf_url":null,"source":{"id":"https://openalex.org/S4306481413","display_name":"Universidad de Chile","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Art\u00edculo de revista"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00180307v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00180307","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2008, 7 (1), pp.33","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320323458","display_name":"Universidad de Chile","ror":"https://ror.org/047gc3g35"},{"id":"https://openalex.org/F4320334812","display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","ror":"https://ror.org/02ap3w078"},{"id":"https://openalex.org/F4320338206","display_name":"Fondo de Financiamiento de Centros de Investigaci\u00f3n en \u00c1reas Prioritarias","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W57709628","https://openalex.org/W579422463","https://openalex.org/W1536365551","https://openalex.org/W1547249381","https://openalex.org/W1646254201","https://openalex.org/W1676467742","https://openalex.org/W1997820336","https://openalex.org/W1998006987","https://openalex.org/W1998926400","https://openalex.org/W2002933529","https://openalex.org/W2002995813","https://openalex.org/W2005566801","https://openalex.org/W2027239222","https://openalex.org/W2062868387","https://openalex.org/W2076666589","https://openalex.org/W2083789154","https://openalex.org/W2085206837","https://openalex.org/W2096131668","https://openalex.org/W2098262645","https://openalex.org/W2116801612","https://openalex.org/W2161108761","https://openalex.org/W2172705324","https://openalex.org/W2175561787","https://openalex.org/W2587764069","https://openalex.org/W3015068942","https://openalex.org/W3021781293","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1629114577","https://openalex.org/W2016131309","https://openalex.org/W1988305515","https://openalex.org/W4226182039","https://openalex.org/W2091201897","https://openalex.org/W2325571063","https://openalex.org/W1538162954","https://openalex.org/W2151489625","https://openalex.org/W2365188296","https://openalex.org/W4288349111"],"abstract_inverted_index":{"We":[0,52,74,125],"study":[1],"the":[2,66,78,94,106,116,131,136,143,147],"asymptotic":[3,56],"behavior":[4],"of":[5,13,31,118,130,153],"a":[6,9,25,49,82,122],"system":[7],"modeling":[8],"composite":[10],"material":[11],"made":[12],"an":[14,119],"elastic":[15,154],"periodically":[16],"perforated":[17],"support,":[18],"with":[19],"period":[20],"$\\varepsilon":[21],">":[22],"0$,":[23],"and":[24,58,97,121],"perfect":[26],"gas":[27],"placed":[28],"in":[29,62,77,115,146],"each":[30],"these":[32],"perforations,":[33],"as":[34,69],"$\\varepsilon$":[35,70],"goes":[36,71],"to":[37,46,64,72,104],"zero.":[38],"The":[39,110],"model":[40],"we":[41,80,92,140],"use":[42],"is":[43,112],"linear,":[44],"corresponding":[45,95],"deformations":[47],"around":[48],"reference":[50],"configuration.":[51],"apply":[53],"both":[54,114],"two-scale":[55,59,83],"expansion":[57],"convergence":[60],"methods":[61],"order":[63],"identify":[65,93],"limit":[67,132],"behaviors":[68],"0.":[73],"state":[75],"that":[76],"limit,":[79],"get":[81],"linear":[84],"elasticity-like":[85],"boundary":[86],"value":[87],"problem.":[88],"From":[89],"this":[90],"problem,":[91],"homogenized":[96,137,144],"periodic":[98],"cell":[99],"equations":[100],"which":[101],"allow":[102],"us":[103],"find":[105],"first":[107],"corrector":[108],"term.":[109],"analysis":[111],"performed":[113],"case":[117,149],"incompressible":[120,148],"compressible":[123],"material.":[124],"derive":[126],"some":[127],"mechanical":[128],"properties":[129],"materials":[133],"by":[134],"studying":[135],"coefficients.":[138],"Finally,":[139],"calculate":[141],"numerically":[142],"coefficients":[145],"for":[150],"different":[151],"types":[152],"materials.":[155]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}