{"id":"https://openalex.org/W4391069985","doi":"https://doi.org/10.1016/j.compstruct.2024.117912","title":"Higher gradient homogenization of quasi-periodic media and applications to inclusion-based composites","display_name":"Higher gradient homogenization of quasi-periodic media and applications to inclusion-based composites","publication_year":2024,"publication_date":"2024-01-21","ids":{"openalex":"https://openalex.org/W4391069985","doi":"https://doi.org/10.1016/j.compstruct.2024.117912"},"language":"en","primary_location":{"id":"doi:10.1016/j.compstruct.2024.117912","doi":"https://doi.org/10.1016/j.compstruct.2024.117912","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.compstruct.2024.117912","pdf_url":null,"source":{"id":"https://openalex.org/S52363224","display_name":"Composite Structures","issn_l":"0263-8223","issn":["0263-8223","1879-1085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Composite Structures","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.compstruct.2024.117912","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082601424","display_name":"Nagham Mawassy","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I160368002","display_name":"Lebanese University","ror":"https://ror.org/05x6qnc69","country_code":"LB","type":"education","lineage":["https://openalex.org/I160368002"]},{"id":"https://openalex.org/I4210115482","display_name":"Laboratoire d'\u00c9tude des Microstructures et de M\u00e9canique des Mat\u00e9riaux","ror":"https://ror.org/01nyrrx14","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I190752583","https://openalex.org/I190861549","https://openalex.org/I4210095849","https://openalex.org/I4210115482","https://openalex.org/I4210134562","https://openalex.org/I4210150706","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR","LB"],"is_corresponding":false,"raw_author_name":"Nagham Mawassy","raw_affiliation_strings":["Faculty of Engineering, Section III, Lebanese University, Campus Rafic Hariri, Beirut, Lebanon","Universit\u00e9 de Lorraine \u2013 CNRS, LEM3, UMR CNRS 7239, 7 rue F\u00e9lix Savart F-57070 Metz, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Section III, Lebanese University, Campus Rafic Hariri, Beirut, Lebanon","institution_ids":["https://openalex.org/I160368002"]},{"raw_affiliation_string":"Universit\u00e9 de Lorraine \u2013 CNRS, LEM3, UMR CNRS 7239, 7 rue F\u00e9lix Savart F-57070 Metz, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210115482","https://openalex.org/I90183372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102777368","display_name":"Seyed Ehsan Alavi","orcid":"https://orcid.org/0000-0002-9148-6645","observed_orcids":["https://orcid.org/0000-0002-9148-6645"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210115482","display_name":"Laboratoire d'\u00c9tude des Microstructures et de M\u00e9canique des Mat\u00e9riaux","ror":"https://ror.org/01nyrrx14","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I190752583","https://openalex.org/I190861549","https://openalex.org/I4210095849","https://openalex.org/I4210115482","https://openalex.org/I4210134562","https://openalex.org/I4210150706","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S.E. Alavi","raw_affiliation_strings":["Universit\u00e9 de Lorraine \u2013 CNRS, LEM3, UMR CNRS 7239, 7 rue F\u00e9lix Savart F-57070 Metz, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine \u2013 CNRS, LEM3, UMR CNRS 7239, 7 rue F\u00e9lix Savart F-57070 Metz, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210115482","https://openalex.org/I90183372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087946017","display_name":"Hilal Reda","orcid":"https://orcid.org/0000-0001-9244-4052","observed_orcids":["https://orcid.org/0000-0001-9244-4052"]},"institutions":[{"id":"https://openalex.org/I160368002","display_name":"Lebanese University","ror":"https://ror.org/05x6qnc69","country_code":"LB","type":"education","lineage":["https://openalex.org/I160368002"]},{"id":"https://openalex.org/I4210104393","display_name":"International University of Beirut","ror":"https://ror.org/01fjkp854","country_code":"LB","type":"education","lineage":["https://openalex.org/I4210104393"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"Hilal Reda","raw_affiliation_strings":["Faculty of Engineering, Section III, Lebanese University, Campus Rafic Hariri, Beirut, Lebanon","SDM Research Group, International University of Beirut BIU, Beirut, Lebanon"],"raw_orcid":"https://orcid.org/0000-0001-9244-4052","affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Section III, Lebanese University, Campus Rafic Hariri, Beirut, Lebanon","institution_ids":["https://openalex.org/I160368002"]},{"raw_affiliation_string":"SDM Research Group, International University of Beirut BIU, Beirut, Lebanon","institution_ids":["https://openalex.org/I4210104393"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060620926","display_name":"Jean\u2010Fran\u00e7ois Ganghoffer","orcid":"https://orcid.org/0000-0002-7947-0587","observed_orcids":["https://orcid.org/0000-0002-7947-0587"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210115482","display_name":"Laboratoire d'\u00c9tude des Microstructures et de M\u00e9canique des Mat\u00e9riaux","ror":"https://ror.org/01nyrrx14","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I190752583","https://openalex.org/I190861549","https://openalex.org/I4210095849","https://openalex.org/I4210115482","https://openalex.org/I4210134562","https://openalex.org/I4210150706","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Francois Ganghoffer","raw_affiliation_strings":["Universit\u00e9 de Lorraine \u2013 CNRS, LEM3, UMR CNRS 7239, 7 rue F\u00e9lix Savart F-57070 Metz, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine \u2013 CNRS, LEM3, UMR CNRS 7239, 7 rue F\u00e9lix Savart F-57070 Metz, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210115482","https://openalex.org/I90183372"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4440,"currency":"USD","value_usd":4440},"apc_paid":{"value":4440,"currency":"USD","value_usd":4440},"fwci":1.1858,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.70088707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"333","issue":null,"first_page":"117912","last_page":"117912"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.6273999810218811,"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"}},"topics":[{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.6273999810218811,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.34060001373291016,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.002300000051036477,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/strain-gradient","display_name":"strain gradient","score":0.4950000047683716},{"id":"https://openalex.org/keywords/effective-moduli","display_name":"effective moduli","score":0.7490000128746033},{"id":"https://openalex.org/keywords/shape-derivative","display_name":"shape derivative","score":0.8149999976158142},{"id":"https://openalex.org/keywords/eshelby-stress","display_name":"Eshelby stress","score":0.8849999904632568},{"id":"https://openalex.org/keywords/unit-cell-geometry","display_name":"unit cell geometry","score":0.5490000247955322},{"id":"https://openalex.org/keywords/periodic-unit-cell","display_name":"periodic unit cell","score":0.5289999842643738},{"id":"https://openalex.org/keywords/surface-integrals","display_name":"surface integrals","score":0.421999990940094}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8936680555343628},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.7109150886535645},{"id":"https://openalex.org/C46581059","wikidata":"https://www.wikidata.org/wiki/Q116301","display_name":"Periodic point","level":2,"score":0.6466510891914368},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.6099031567573547},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.586333155632019},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5202214121818542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5197839140892029},{"id":"https://openalex.org/C98644592","wikidata":"https://www.wikidata.org/wiki/Q184743","display_name":"Periodic function","level":2,"score":0.45145782828330994},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.44907552003860474},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3391360640525818},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28993329405784607},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.compstruct.2024.117912","doi":"https://doi.org/10.1016/j.compstruct.2024.117912","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.compstruct.2024.117912","pdf_url":null,"source":{"id":"https://openalex.org/S52363224","display_name":"Composite Structures","issn_l":"0263-8223","issn":["0263-8223","1879-1085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Composite Structures","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05732133v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.univ-lorraine.fr/hal-05732133","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Composite Structures, 2024, 333, pp.117912. ⟨10.1016/j.compstruct.2024.117912⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1016/j.compstruct.2024.117912","doi":"https://doi.org/10.1016/j.compstruct.2024.117912","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.compstruct.2024.117912","pdf_url":null,"source":{"id":"https://openalex.org/S52363224","display_name":"Composite Structures","issn_l":"0263-8223","issn":["0263-8223","1879-1085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Composite Structures","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W874556551","https://openalex.org/W1559840026","https://openalex.org/W1935684211","https://openalex.org/W1974025340","https://openalex.org/W1980679962","https://openalex.org/W1994144821","https://openalex.org/W2008588630","https://openalex.org/W2016150461","https://openalex.org/W2021000520","https://openalex.org/W2027239222","https://openalex.org/W2042676776","https://openalex.org/W2043130099","https://openalex.org/W2043425930","https://openalex.org/W2045972744","https://openalex.org/W2051750157","https://openalex.org/W2051961749","https://openalex.org/W2052055030","https://openalex.org/W2062325236","https://openalex.org/W2092939767","https://openalex.org/W2098871123","https://openalex.org/W2105880720","https://openalex.org/W2136993027","https://openalex.org/W2156956713","https://openalex.org/W2478917285","https://openalex.org/W2491281109","https://openalex.org/W2558887067","https://openalex.org/W2566560133","https://openalex.org/W2763808526","https://openalex.org/W2808992770","https://openalex.org/W2894044830","https://openalex.org/W2907341700","https://openalex.org/W2907634188","https://openalex.org/W2955896699","https://openalex.org/W2956114328","https://openalex.org/W3033896014","https://openalex.org/W3092602958","https://openalex.org/W3129435632","https://openalex.org/W3132975319","https://openalex.org/W3207711198","https://openalex.org/W4247177829","https://openalex.org/W4297832350","https://openalex.org/W4307419837","https://openalex.org/W4320480760","https://openalex.org/W7150732083"],"related_works":["https://openalex.org/W4403490074","https://openalex.org/W7010113380","https://openalex.org/W4402572526","https://openalex.org/W2973253802","https://openalex.org/W2907634188","https://openalex.org/W2599784814","https://openalex.org/W2073520457","https://openalex.org/W2184522376","https://openalex.org/W1996752800","https://openalex.org/W2790827003"],"abstract_inverted_index":{"This":[0,111,231,271],"paper":[1,69],"introduces":[2],"quasi-periodic":[3,7,60,137,151,210,286],"homogenization":[4,24,61,307],"schemes":[5,308],"for":[6,311],"media,":[8],"those":[9,166],"without":[10],"strict":[11],"periodicity,":[12],"but":[13],"that":[14],"can":[15],"be":[16],"mapped":[17],"to":[18,35,106,248,276,283],"a":[19,32,36,41,79,84,119,176,182,195,205,236,280,326],"parent":[20],"periodic":[21,38,133,173,245],"medium.":[22],"Quasi-periodic":[23],"relies":[25,70,233],"on":[26,71,215,234,298],"the":[27,48,64,73,87,95,99,107,115,124,128,132,136,160,163,172,189,199,209,216,222,228,241,244,254,262,268,277,285,292,295,299,305,315,323,329],"conceptual":[28],"idea":[29],"of":[30,44,50,59,67,76,86,92,94,102,109,123,131,141,162,171,202,208,218,221,243,257,267,294,304,317,325,328],"mapping":[31,43],"non-periodic":[33],"domain":[34,49,193],"reference":[37,190],"one":[39,138,279],"through":[40],"point":[42],"material":[45],"points":[46],"within":[47,78,227],"an":[51,142],"identified":[52],"repetitive":[53],"unit":[54,81,96,191,229,246,269,300,330],"cell.":[55,230,270],"The":[56,150],"theoretical":[57],"background":[58],"introduced":[62],"in":[63,139,169,181,194,322],"first":[65,278],"part":[66,201],"this":[68,203],"expressing":[72],"microscopic":[74,148,164],"position":[75,89,101],"micropoints":[77,103],"physical":[80],"cell":[82,192,247,301,331],"as":[83,185,288],"sum":[85],"macroscopic":[88,146],"(the":[90],"center":[91,108],"area":[93],"cell)":[97],"and":[98,147,175,264],"relative":[100],"with":[104],"respect":[105],"area.":[110],"decomposition":[112,122,144],"parameterized":[113],"by":[114,253],"small-scale":[116],"parameter":[117],"entails":[118],"corresponding":[120],"additive":[121,143],"tangent":[125],"map":[126],"defining":[127],"geometrical":[129],"transformation":[130],"UC":[134],"into":[135,145],"terms":[140,170],"contributions.":[149],"homogenized":[152],"effective":[153],"moduli":[154,174,211,287],"are":[155,309],"then":[156],"determined,":[157],"starting":[158],"from":[159],"average":[161],"energy,":[165],"being":[167],"expressed":[168,180],"perturbation":[177],"term,":[178],"both":[179,261],"volumetric":[183],"format":[184],"surface":[186,206],"integrals":[187],"over":[188],"2D":[196],"context.":[197],"In":[198],"second":[200,272],"contribution,":[204],"formulation":[207],"is":[212],"derived,":[213],"based":[214],"notion":[217],"shape":[219,237],"derivative":[220],"total":[223],"potential":[224],"energy":[225],"stored":[226],"approach":[232],"introducing":[235],"velocity":[238],"field":[239],"at":[240],"boundary":[242],"change":[249],"its":[250],"design,":[251],"driven":[252],"normal":[255],"projection":[256],"Eshelby":[258],"stress":[259],"onto":[260],"internal":[263],"external":[265],"boundaries":[266],"scheme":[273],"offers":[274],"comparatively":[275],"simpler":[281],"way":[282],"compute":[284],"it":[289],"only":[290],"requires":[291],"evaluation":[293],"mechanical":[296],"fields":[297],"boundaries.":[302],"Application":[303],"proposed":[306],"done":[310],"inclusion-based":[312],"composites,":[313],"underlining":[314],"importance":[316],"strain":[318],"gradient":[319],"energetic":[320],"contribution":[321],"situation":[324],"micrograding":[327],"geometry.":[332]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2024-01-22T00:00:00"}