{"id":"https://openalex.org/W1974958167","doi":"https://doi.org/10.1137/060676520","title":"Local Field Assessment inside Multiscale Composite Architectures","display_name":"Local Field Assessment inside Multiscale Composite Architectures","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1974958167","doi":"https://doi.org/10.1137/060676520","mag":"1974958167"},"language":"en","primary_location":{"id":"doi:10.1137/060676520","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060676520","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 &amp; Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049232981","display_name":"Timothy Breitzman","orcid":"https://orcid.org/0009-0007-6471-4933"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Timothy Breitzman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040697039","display_name":"Robert Lipton","orcid":"https://orcid.org/0000-0002-1382-3204"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Lipton","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108831824","display_name":"Endel V. Iarve","orcid":"https://orcid.org/0009-0003-7999-2224"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Endel Iarve","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049232981"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7695,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.87931156,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"6","issue":"3","first_page":"937","last_page":"962"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":1.0,"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":1.0,"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":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"}}],"keywords":[{"id":"https://openalex.org/keywords/composite-number","display_name":"Composite number","score":0.7568936944007874},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5411268472671509},{"id":"https://openalex.org/keywords/stress-field","display_name":"Stress field","score":0.5072355270385742},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4721405804157257},{"id":"https://openalex.org/keywords/local-field","display_name":"Local field","score":0.4584256410598755},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.451462060213089},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.4433036148548126},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.44096362590789795},{"id":"https://openalex.org/keywords/stress","display_name":"Stress (linguistics)","score":0.42208725214004517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3872985243797302},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.3686363101005554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3546179533004761},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33787572383880615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3244956135749817},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.3113101124763489},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.2558659017086029},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.235213041305542},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2148614227771759},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18326535820960999},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.12894606590270996}],"concepts":[{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.7568936944007874},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5411268472671509},{"id":"https://openalex.org/C2778414698","wikidata":"https://www.wikidata.org/wiki/Q7623438","display_name":"Stress field","level":3,"score":0.5072355270385742},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4721405804157257},{"id":"https://openalex.org/C84583765","wikidata":"https://www.wikidata.org/wiki/Q1868517","display_name":"Local field","level":2,"score":0.4584256410598755},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.451462060213089},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.4433036148548126},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.44096362590789795},{"id":"https://openalex.org/C21036866","wikidata":"https://www.wikidata.org/wiki/Q181767","display_name":"Stress (linguistics)","level":2,"score":0.42208725214004517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3872985243797302},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3686363101005554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3546179533004761},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33787572383880615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3244956135749817},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.3113101124763489},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2558659017086029},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.235213041305542},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2148614227771759},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18326535820960999},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.12894606590270996},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060676520","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060676520","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 &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.lsu.edu:mathematics_pubs-1736","is_oa":false,"landing_page_url":"https://digitalcommons.lsu.edu/mathematics_pubs/737","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:repository.lsu.edu:mathematics_pubs-1736","is_oa":false,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/737","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.7799999713897705,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W360968607","https://openalex.org/W1491392068","https://openalex.org/W1496258437","https://openalex.org/W1547249381","https://openalex.org/W1676467742","https://openalex.org/W1966353319","https://openalex.org/W1966480196","https://openalex.org/W1977502308","https://openalex.org/W1978693661","https://openalex.org/W1990157709","https://openalex.org/W1995945277","https://openalex.org/W2005310731","https://openalex.org/W2010552982","https://openalex.org/W2010614078","https://openalex.org/W2018285721","https://openalex.org/W2023701895","https://openalex.org/W2027179062","https://openalex.org/W2029918260","https://openalex.org/W2030604754","https://openalex.org/W2030844752","https://openalex.org/W2034252667","https://openalex.org/W2038330765","https://openalex.org/W2044011197","https://openalex.org/W2052161587","https://openalex.org/W2067614753","https://openalex.org/W2071903075","https://openalex.org/W2072515857","https://openalex.org/W2074917656","https://openalex.org/W2078045751","https://openalex.org/W2080998493","https://openalex.org/W2084749716","https://openalex.org/W2099103066","https://openalex.org/W2115144158","https://openalex.org/W2118723192","https://openalex.org/W2127004824","https://openalex.org/W2133066748","https://openalex.org/W2137746982","https://openalex.org/W2138328034","https://openalex.org/W2154905879","https://openalex.org/W2168522132","https://openalex.org/W2206315619","https://openalex.org/W2325830745","https://openalex.org/W3214098784","https://openalex.org/W4235868234","https://openalex.org/W4248758651"],"related_works":["https://openalex.org/W2560215812","https://openalex.org/W2949601986","https://openalex.org/W2788972299","https://openalex.org/W2521347458","https://openalex.org/W2498789492","https://openalex.org/W2729981612","https://openalex.org/W2925692864","https://openalex.org/W4233449973","https://openalex.org/W3092410375","https://openalex.org/W2419034073"],"abstract_inverted_index":{"We":[0],"introduce":[1],"asymptotic":[2,43,103],"expansions":[3,44],"for":[4,105],"recovering":[5],"the":[6,15,29,34,76,81,84,91,99,102,108],"local":[7,55,85,113],"field":[8,56,114],"behavior":[9],"inside":[10,38,58,90,116],"multiscale":[11],"composite":[12,30,118],"architectures":[13],"in":[14,28],"presence":[16],"of":[17,73,83,101,112],"residual":[18],"stress.":[19],"The":[20,42],"theory":[21,104],"applies":[22],"to":[23,47,53,64,66,97],"zones":[24],"containing":[25],"abrupt":[26],"changes":[27],"microgeometry.":[31],"This":[32],"includes":[33],"interfaces":[35],"between":[36],"plies":[37],"fiber":[39],"reinforced":[40],"laminates.":[41],"are":[45,95],"used":[46],"develop":[48],"a":[49,59,67],"fast":[50],"numerical":[51,69],"algorithm":[52],"extract":[54],"information":[57],"prescribed":[60],"subdomain":[61],"without":[62],"having":[63],"resort":[65],"full":[68],"simulation.":[70],"For":[71],"regions":[72],"homogeneous":[74],"microstructure,":[75],"analysis":[77],"delivers":[78],"bounds":[79],"on":[80],"magnitude":[82,111],"stress":[86],"and":[87,110],"strain":[88],"fields":[89],"composite.":[92],"Numerical":[93],"examples":[94],"provided":[96],"demonstrate":[98],"utility":[100],"quickly":[106],"assessing":[107],"location":[109],"concentrations":[115],"complex":[117],"architectures.":[119]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
