{"id":"https://openalex.org/W2120271468","doi":"https://doi.org/10.1137/060672790","title":"Two-Scale Homogenization for Evolutionary Variational Inequalities via the Energetic Formulation","display_name":"Two-Scale Homogenization for Evolutionary Variational Inequalities via the Energetic Formulation","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2120271468","doi":"https://doi.org/10.1137/060672790","mag":"2120271468"},"language":"en","primary_location":{"id":"doi:10.1137/060672790","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060672790","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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":"SIAM Journal on Mathematical Analysis","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/A5052253534","display_name":"Alexander Mielke","orcid":"https://orcid.org/0000-0002-4583-3888"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alexander Mielke","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081279855","display_name":"Aida Timofte","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aida M. Timofte","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052253534"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.23,"has_fulltext":false,"cited_by_count":83,"citation_normalized_percentile":{"value":0.95672055,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"39","issue":"2","first_page":"642","last_page":"668"},"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":0.9995999932289124,"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":0.9991000294685364,"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":0.8551404476165771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8185303211212158},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5601133108139038},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5527921915054321},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.5398011207580566},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5069966316223145},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.47917237877845764},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.47076988220214844},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.4396754503250122},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41384539008140564},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.41193076968193054},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3359631299972534},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11230510473251343}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8551404476165771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8185303211212158},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5601133108139038},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5527921915054321},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.5398011207580566},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5069966316223145},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.47917237877845764},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.47076988220214844},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.4396754503250122},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41384539008140564},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.41193076968193054},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3359631299972534},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11230510473251343},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060672790","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060672790","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:doi:10.20347/wias.preprint.1172","is_oa":false,"landing_page_url":"http://localhost:8291/receive/wias_mods_00001424","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":null,"raw_type":"preprint"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6499999761581421,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W99391655","https://openalex.org/W269471861","https://openalex.org/W1518297095","https://openalex.org/W1537639429","https://openalex.org/W1553150814","https://openalex.org/W1596635901","https://openalex.org/W1967203031","https://openalex.org/W1972892940","https://openalex.org/W1974309308","https://openalex.org/W1974468611","https://openalex.org/W1981529167","https://openalex.org/W1983429394","https://openalex.org/W1986664864","https://openalex.org/W1989046305","https://openalex.org/W1993654840","https://openalex.org/W2003313595","https://openalex.org/W2007321609","https://openalex.org/W2023874008","https://openalex.org/W2026899601","https://openalex.org/W2027239222","https://openalex.org/W2037087394","https://openalex.org/W2045069146","https://openalex.org/W2049893929","https://openalex.org/W2056773849","https://openalex.org/W2062676931","https://openalex.org/W2066179673","https://openalex.org/W2076116127","https://openalex.org/W2082346574","https://openalex.org/W2096165789","https://openalex.org/W2110689112","https://openalex.org/W2116801612","https://openalex.org/W2134166909","https://openalex.org/W2521513830","https://openalex.org/W2897725581","https://openalex.org/W2953094344","https://openalex.org/W3022489451","https://openalex.org/W3142812456","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3162077676","https://openalex.org/W2623225148","https://openalex.org/W1969373293","https://openalex.org/W2734680054","https://openalex.org/W2405202699","https://openalex.org/W2385030590","https://openalex.org/W2273702765","https://openalex.org/W2066249546","https://openalex.org/W2019676222","https://openalex.org/W2036915488"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,50,68,77,160],"devoted":[3],"to":[4,51,64,162,173],"two-scale":[5,106,120],"homogenization":[6],"for":[7,56,150],"a":[8,53,82,94,118],"class":[9],"of":[10,32,73,81,89,102,148,167],"rate-independent":[11],"systems":[12],"described":[13],"by":[14,20],"the":[15,29,48,57,61,71,98,125,129,135,139,151,165,168,174,179],"energetic":[16,74,152,175],"formulation":[17,153],"or":[18],"equivalently":[19],"an":[21,86,90,145],"evolutionary":[22],"variational":[23],"inequality.":[24],"In":[25],"particular,":[26],"we":[27,111],"treat":[28],"classical":[30],"model":[31],"linearized":[33],"elastoplasticity":[34],"with":[35,170,178],"hardening.":[36],"The":[37],"associated":[38,177],"nonlinear":[39],"partial":[40],"differential":[41],"inclusion":[42],"has":[43],"periodically":[44],"oscillating":[45],"coefficients,":[46],"and":[47,85,93,104],"aim":[49],"find":[52],"limit":[54,180],"problem":[55,169],"case":[58],"in":[59,79,128,138],"which":[60,76],"period":[62],"tends":[63],"0.":[65],"Our":[66],"approach":[67],"based":[69],"on":[70,144],"notion":[72],"solutions,":[75],"phrased":[78],"terms":[80],"stability":[83],"condition":[84],"energy":[87],"balance":[88],"energy-storage":[91],"functional":[92],"dissipation":[95],"functional.":[96],"Using":[97],"recently":[99],"developed":[100],"method":[101],"weak":[103],"strong":[105],"convergence":[107],"via":[108],"periodic":[109],"unfolding,":[110],"show":[112,163],"that":[113,164],"these":[114],"two":[115],"functionals":[116],"have":[117],"suitable":[119],"limit,":[121],"but":[122],"now":[123],"involving":[124],"macroscopic":[126],"variable":[127,137],"physical":[130],"domain":[131],"as":[132,134],"well":[133],"microscopic":[136],"periodicity":[140,171],"cell.":[141],"Moreover,":[142],"relying":[143],"abstract":[146],"theory":[147],"$\\Gamma$-convergence":[149],"using":[154],"so-called":[155],"joint":[156],"recovery":[157],"sequences,":[158],"it":[159],"possible":[161],"solutions":[166],"converge":[172],"solution":[176],"functionals.":[181]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
