{"id":"https://openalex.org/W2006095326","doi":"https://doi.org/10.1615/intjmultcompeng.v4.i4.80","title":"Study of Various Estimates of the Macroscopic Tangent Operator in the Incremental Homogenization of Elastoplastic Composites","display_name":"Study of Various Estimates of the Macroscopic Tangent Operator in the Incremental Homogenization of Elastoplastic Composites","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2006095326","doi":"https://doi.org/10.1615/intjmultcompeng.v4.i4.80","mag":"2006095326"},"language":"en","primary_location":{"id":"doi:10.1615/intjmultcompeng.v4.i4.80","doi":"https://doi.org/10.1615/intjmultcompeng.v4.i4.80","is_oa":false,"landing_page_url":"https://doi.org/10.1615/intjmultcompeng.v4.i4.80","pdf_url":null,"source":{"id":"https://openalex.org/S63368048","display_name":"International Journal for Multiscale Computational Engineering","issn_l":"1543-1649","issn":["1543-1649","1940-4352"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315730","host_organization_name":"Begell House","host_organization_lineage":["https://openalex.org/P4310315730"],"host_organization_lineage_names":["Begell House"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal for Multiscale Computational Engineering","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5022921957","display_name":"Olivier Pi\u00e9rard","orcid":"https://orcid.org/0000-0002-8441-2568","observed_orcids":["https://orcid.org/0000-0002-8441-2568"]},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Olivier Pierard","raw_affiliation_strings":["Universit\u00e9 Catholique de Louvain (UCL), CESAME, 4 Avenue G. Lema\u00eetre, B-1348 Louvain-la-Neuve, Belgium","Catholique de Louvain (UCL), CESAME, 4 Avenue G. Lema&#238","Universit&#233","tre, B-1348 Louvain-la-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Catholique de Louvain (UCL), CESAME, 4 Avenue G. Lema\u00eetre, B-1348 Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]},{"raw_affiliation_string":"Catholique de Louvain (UCL), CESAME, 4 Avenue G. Lema&#238","institution_ids":["https://openalex.org/I95674353"]},{"raw_affiliation_string":"Universit&#233","institution_ids":[]},{"raw_affiliation_string":"tre, B-1348 Louvain-la-Neuve, Belgium","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071019686","display_name":"Issam Doghri","orcid":"https://orcid.org/0000-0001-8297-1297","observed_orcids":["https://orcid.org/0000-0001-8297-1297"]},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Issam Doghri","raw_affiliation_strings":["Universit\u00e9 Catholique de Louvain (UCL), CESAME, 4 Avenue G. Lema\u00eetre, B-1348 Louvain-la-Neuve, Belgium","Catholique de Louvain (UCL), CESAME, 4 Avenue G. Lema&#238","Universit&#233","tre, B-1348 Louvain-la-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Catholique de Louvain (UCL), CESAME, 4 Avenue G. Lema\u00eetre, B-1348 Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]},{"raw_affiliation_string":"Catholique de Louvain (UCL), CESAME, 4 Avenue G. Lema&#238","institution_ids":["https://openalex.org/I95674353"]},{"raw_affiliation_string":"Universit&#233","institution_ids":[]},{"raw_affiliation_string":"tre, B-1348 Louvain-la-Neuve, Belgium","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I95674353"],"apc_list":null,"apc_paid":null,"fwci":3.8387,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.92007667,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"4","issue":"4","first_page":"521","last_page":"543"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9887999892234802,"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":0.9887999892234802,"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":0.00860000029206276,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.0003000000142492354,"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/mean-field-homogenization","display_name":"mean-field homogenization","score":0.9110000133514404},{"id":"https://openalex.org/keywords/two-phase-composites","display_name":"two-phase composites","score":0.925000011920929},{"id":"https://openalex.org/keywords/anisotropic-inclusions","display_name":"anisotropic inclusions","score":0.7149999737739563},{"id":"https://openalex.org/keywords/plasticity","display_name":"plasticity","score":0.3190000057220459}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.9524105787277222},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.8156341314315796},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.7701931595802307},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.6229721903800964},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5468021631240845},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5093680620193481},{"id":"https://openalex.org/C101842124","wikidata":"https://www.wikidata.org/wiki/Q2449817","display_name":"Transverse isotropy","level":3,"score":0.46925780177116394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44525039196014404},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43525511026382446},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.34956222772598267},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2233249545097351},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17754754424095154},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1615/intjmultcompeng.v4.i4.80","doi":"https://doi.org/10.1615/intjmultcompeng.v4.i4.80","is_oa":false,"landing_page_url":"https://doi.org/10.1615/intjmultcompeng.v4.i4.80","pdf_url":null,"source":{"id":"https://openalex.org/S63368048","display_name":"International Journal for Multiscale Computational Engineering","issn_l":"1543-1649","issn":["1543-1649","1940-4352"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315730","host_organization_name":"Begell House","host_organization_lineage":["https://openalex.org/P4310315730"],"host_organization_lineage_names":["Begell House"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal for Multiscale Computational Engineering","raw_type":"journal-article"},{"id":"pmh:oai:dial.uclouvain.be:boreal:37806","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/37806","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de p\u00c3\u00a9riodique (Journal article)"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4412075676","https://openalex.org/W1700243946","https://openalex.org/W2193103880","https://openalex.org/W1983034596","https://openalex.org/W1734574656","https://openalex.org/W4387760877","https://openalex.org/W2081498196","https://openalex.org/W2306912532","https://openalex.org/W2260378622","https://openalex.org/W2055184999"],"abstract_inverted_index":{"This":[0],"paper":[1],"contains":[2],"a":[3,48,89,114],"theoretical":[4,107],"and":[5,27,57,61,109],"numerical":[6],"investigation":[7],"of":[8,16,24,33,64,92,98],"the":[9,13,25,65,106],"incremental":[10],"formulation":[11,26],"for":[12,47],"mean-field":[14],"homogenization":[15],"two-phase":[17],"elastoplastic":[18],"composites.":[19],"We":[20,42],"study":[21],"several":[22],"variants":[23],"try":[28],"to":[29],"understand":[30],"why":[31],"some":[32,77],"them":[34],"give":[35],"good":[36],"predictions":[37],"while":[38],"others":[39],"do":[40],"not.":[41],"define":[43],"six":[44],"instantaneous":[45],"operators":[46],"fictitious":[49],"homogeneous":[50],"reference":[51],"matrix":[52],"(two":[53],"anisotropic,":[54],"two":[55,58],"isotropic,":[56],"transversely":[59],"isotropic)":[60],"various":[62,101],"estimates":[63,78],"macroscopic":[66],"tangent":[67],"operator.":[68],"Theoretically,":[69],"we":[70,86],"present":[71],"mathematical":[72],"results":[73,108],"that":[74,76],"prove":[75],"are":[79],"stiffer":[80],"or":[81],"softer":[82],"than":[83],"others.":[84],"Numerically,":[85],"carry":[87],"out":[88],"wide":[90],"range":[91],"validated":[93],"simulations":[94],"with":[95],"different":[96],"types":[97],"inclusions":[99],"under":[100],"loads.":[102],"The":[103],"findings":[104],"confirm":[105],"shed":[110],"new":[111],"light":[112],"on":[113],"rather":[115],"complicated":[116],"problem.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2016-06-24T00:00:00"}
