{"id":"https://openalex.org/W4409897297","doi":"https://doi.org/10.1137/23m1584861","title":"Phase-Field Topology Optimization with Periodic Microstructure","display_name":"Phase-Field Topology Optimization with Periodic Microstructure","publication_year":2025,"publication_date":"2025-04-28","ids":{"openalex":"https://openalex.org/W4409897297","doi":"https://doi.org/10.1137/23m1584861"},"language":"en","primary_location":{"id":"doi:10.1137/23m1584861","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1584861","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5074702338","display_name":"Stefano Almi","orcid":"https://orcid.org/0000-0001-7308-221X"},"institutions":[{"id":"https://openalex.org/I4210106463","display_name":"System Science Applications (United States)","ror":"https://ror.org/01gg29e32","country_code":"US","type":"company","lineage":["https://openalex.org/I4210106463"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stefano Almi","raw_affiliation_strings":["Department of Mathematics and Applications R. Caccioppoli, via Cintia, Monte S. Angelo, 80126 Naples, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7308-221X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applications R. Caccioppoli, via Cintia, Monte S. Angelo, 80126 Naples, Italy","institution_ids":["https://openalex.org/I4210106463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087439841","display_name":"Ulisse Stefanelli","orcid":"https://orcid.org/0000-0002-3969-2716"},"institutions":[{"id":"https://openalex.org/I4210137033","display_name":"Istituto di Matematica Applicata e Tecnologie Informatiche","ror":"https://ror.org/03m0n3c07","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210137033","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Ulisse Stefanelli","raw_affiliation_strings":["Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria, Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, W\u00e4hringerstra\u00dfe 17, 1090 Wien, Austria, & Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, via Ferrata 1, I-27100 Pavia, Italy"],"raw_orcid":"https://orcid.org/0000-0002-3969-2716","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria, Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, W\u00e4hringerstra\u00dfe 17, 1090 Wien, Austria, & Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, via Ferrata 1, I-27100 Pavia, Italy","institution_ids":["https://openalex.org/I4210137033"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06394615,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"2","first_page":"1458","last_page":"1484"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998000264167786,"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":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7394516468048096},{"id":"https://openalex.org/keywords/topology-optimization","display_name":"Topology optimization","score":0.6204432845115662},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5949895977973938},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.5078423619270325},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4565010964870453},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3552297353744507},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24792608618736267},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1529335081577301},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1446458101272583},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10969170928001404}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7394516468048096},{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.6204432845115662},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5949895977973938},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.5078423619270325},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4565010964870453},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3552297353744507},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24792608618736267},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1529335081577301},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1446458101272583},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10969170928001404},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1584861","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1584861","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.46000000834465027,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1443340491","display_name":null,"funder_award_id":"10.55776/I-5149","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G1788048472","display_name":"Brittle fracture on plates and shells","funder_award_id":"ESP61","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G1874798228","display_name":null,"funder_award_id":"10.55776/P-32788","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2745783891","display_name":null,"funder_award_id":"10.55776/I4354","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3878859087","display_name":null,"funder_award_id":"10.55776/F65","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7416782364","display_name":"Alternate minimization in fracture mechanics","funder_award_id":"P 35359","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W124257918","https://openalex.org/W124363235","https://openalex.org/W1480714962","https://openalex.org/W1982739078","https://openalex.org/W1985847082","https://openalex.org/W1990541396","https://openalex.org/W2027239222","https://openalex.org/W2069041228","https://openalex.org/W2085115947","https://openalex.org/W2095072431","https://openalex.org/W2098130716","https://openalex.org/W2153300317","https://openalex.org/W2162526242","https://openalex.org/W2228170291","https://openalex.org/W2265329769","https://openalex.org/W2327409378","https://openalex.org/W2333053272","https://openalex.org/W2726058428","https://openalex.org/W2766801072","https://openalex.org/W2793241137","https://openalex.org/W2950547113","https://openalex.org/W2978906913","https://openalex.org/W3005211765","https://openalex.org/W3036052859","https://openalex.org/W3039290975","https://openalex.org/W3080508343","https://openalex.org/W3091843051","https://openalex.org/W3112925457","https://openalex.org/W3121344092","https://openalex.org/W3122760352","https://openalex.org/W3134775088","https://openalex.org/W3140078684","https://openalex.org/W3195023627","https://openalex.org/W3216512607","https://openalex.org/W4205997767","https://openalex.org/W4233371490","https://openalex.org/W4249480917","https://openalex.org/W4321252244","https://openalex.org/W4323076564","https://openalex.org/W4324295257","https://openalex.org/W4367833610","https://openalex.org/W4386418435"],"related_works":["https://openalex.org/W2046491619","https://openalex.org/W2389142552","https://openalex.org/W2239929624","https://openalex.org/W2883804989","https://openalex.org/W1974803732","https://openalex.org/W2008556190","https://openalex.org/W2081304691","https://openalex.org/W2127556255","https://openalex.org/W3018492858","https://openalex.org/W279903623"],"abstract_inverted_index":{"Abstract.":[0],"Progress":[1],"in":[2],"additive":[3],"manufacturing":[4],"technologies":[5],"allows":[6],"the":[7,20,30,34,81,86,97,102],"realization":[8],"of":[9,25,33,69],"finely":[10],"graded":[11],"microstructured":[12],"materials":[13],"with":[14],"tunable":[15],"mechanical":[16,36],"properties.":[17],"This":[18],"paves":[19],"way":[21],"to":[22,74],"a":[23,47,56,66],"wealth":[24],"innovative":[26],"applications,":[27],"calling":[28],"for":[29,51],"combined":[31],"design":[32],"macroscopic":[35],"piece":[37],"and":[38,84,100],"its":[39],"underlying":[40],"microstructure.":[41,58],"In":[42],"this":[43],"context,":[44],"we":[45,79],"investigate":[46,85],"topology":[48],"optimization":[49,60],"problem":[50,61,83],"an":[52],"elastic":[53],"medium":[54],"featuring":[55],"periodic":[57],"The":[59],"is":[62],"variationally":[63],"formulated":[64],"as":[65],"bilevel":[67],"minimization":[68],"phase-field":[70,99],"type.":[71],"By":[72],"resorting":[73],"[Formula:":[75],"see":[76],"text]-convergence":[77],"techniques,":[78],"characterize":[80],"homogenized":[82,98],"corresponding":[87],"sharp-interface":[88,103],"limit.":[89],"First-order":[90],"optimality":[91],"conditions":[92],"are":[93],"derived,":[94],"both":[95],"at":[96,101],"levels.":[104]},"counts_by_year":[],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}
