{"id":"https://openalex.org/W1983321528","doi":"https://doi.org/10.1007/s10957-012-0094-6","title":"Optimal Design of Brittle Composite Materials: a Nonsmooth Approach","display_name":"Optimal Design of Brittle Composite Materials: a Nonsmooth Approach","publication_year":2012,"publication_date":"2012-06-15","ids":{"openalex":"https://openalex.org/W1983321528","doi":"https://doi.org/10.1007/s10957-012-0094-6","mag":"1983321528"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-012-0094-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-012-0094-6","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","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/A5080459402","display_name":"M. Prechtel","orcid":null},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Marina Prechtel","raw_affiliation_strings":["Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany","Department of Mathematics, University of Erlangen-Nuremberg, Martensstr. 3, 91058, Erlangen, Germany","University of Erlangen-Nuremberg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Department of Mathematics, University of Erlangen-Nuremberg, Martensstr. 3, 91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"University of Erlangen-Nuremberg","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072544377","display_name":"G\u00fcnter Leugering","orcid":"https://orcid.org/0000-0002-1086-991X"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"G\u00fcnter Leugering","raw_affiliation_strings":["Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany","Department of Mathematics, University of Erlangen-Nuremberg, Martensstr. 3, 91058, Erlangen, Germany","University of Erlangen-Nuremberg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Department of Mathematics, University of Erlangen-Nuremberg, Martensstr. 3, 91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"University of Erlangen-Nuremberg","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055353787","display_name":"Paul Steinmann","orcid":"https://orcid.org/0000-0003-1490-947X"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Paul Steinmann","raw_affiliation_strings":["Department of Mechanical Engineering, University of Erlangen-Nuremberg, Egerlandstr. 5, 91058, Erlangen, Germany","Department of Mechanical Engineering, University of Erlangen-Nuremberg, Erlangen, Germany","University of Erlangen-Nuremberg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Erlangen-Nuremberg, Egerlandstr. 5, 91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Department of Mechanical Engineering, University of Erlangen-Nuremberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"University of Erlangen-Nuremberg","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013459854","display_name":"Michael Stingl","orcid":"https://orcid.org/0000-0002-3626-0723"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michael Stingl","raw_affiliation_strings":["Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany","Department of Mathematics, University of Erlangen-Nuremberg, N\u00e4gelsbachstr. 49b, 91052, Erlangen, Germany","University of Erlangen-Nuremberg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Department of Mathematics, University of Erlangen-Nuremberg, N\u00e4gelsbachstr. 49b, 91052, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"University of Erlangen-Nuremberg","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5013459854","https://openalex.org/A5055353787","https://openalex.org/A5072544377","https://openalex.org/A5080459402"],"corresponding_institution_ids":["https://openalex.org/I181369854"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.6435,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73591883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"155","issue":"3","first_page":"962","last_page":"985"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9998999834060669,"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":0.9998999834060669,"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/T11558","display_name":"Composite Material Mechanics","score":0.9998999834060669,"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/T10221","display_name":"Composite Structure Analysis and Optimization","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"}}],"keywords":[{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.6658535003662109},{"id":"https://openalex.org/keywords/brittleness","display_name":"Brittleness","score":0.6576404571533203},{"id":"https://openalex.org/keywords/displacement-field","display_name":"Displacement field","score":0.6306418180465698},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6001899242401123},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5309405326843262},{"id":"https://openalex.org/keywords/fracture","display_name":"Fracture (geology)","score":0.48771342635154724},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4588187336921692},{"id":"https://openalex.org/keywords/composite-number","display_name":"Composite number","score":0.41608816385269165},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3395991623401642},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.24133187532424927},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.16571226716041565},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.14974981546401978},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.12289953231811523},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07618996500968933},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0714663565158844},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06882640719413757}],"concepts":[{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.6658535003662109},{"id":"https://openalex.org/C136478896","wikidata":"https://www.wikidata.org/wiki/Q898288","display_name":"Brittleness","level":2,"score":0.6576404571533203},{"id":"https://openalex.org/C29660869","wikidata":"https://www.wikidata.org/wiki/Q5282615","display_name":"Displacement field","level":3,"score":0.6306418180465698},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6001899242401123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5309405326843262},{"id":"https://openalex.org/C43369102","wikidata":"https://www.wikidata.org/wiki/Q2307625","display_name":"Fracture (geology)","level":2,"score":0.48771342635154724},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4588187336921692},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.41608816385269165},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3395991623401642},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.24133187532424927},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.16571226716041565},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.14974981546401978},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.12289953231811523},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07618996500968933},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0714663565158844},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06882640719413757},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10957-012-0094-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-012-0094-6","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:155:y:2012:i:3:d:10.1007_s10957-012-0094-6","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-012-0094-6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:eprints.gla.ac.uk:192243","is_oa":false,"landing_page_url":"http://eprints.gla.ac.uk/192243/","pdf_url":null,"source":{"id":"https://openalex.org/S4210235606","display_name":"ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam)","issn_l":"2622-8912","issn":["2622-8912","2622-8920"],"is_oa":false,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W4075705","https://openalex.org/W9266416","https://openalex.org/W117140004","https://openalex.org/W160043448","https://openalex.org/W175969631","https://openalex.org/W410560092","https://openalex.org/W566531027","https://openalex.org/W1485606643","https://openalex.org/W1491720843","https://openalex.org/W1516415680","https://openalex.org/W1516519565","https://openalex.org/W1522022671","https://openalex.org/W1604627832","https://openalex.org/W1719686946","https://openalex.org/W1966970605","https://openalex.org/W1968658640","https://openalex.org/W1970101292","https://openalex.org/W1975140172","https://openalex.org/W1981552546","https://openalex.org/W2008896163","https://openalex.org/W2009604356","https://openalex.org/W2019810393","https://openalex.org/W2029892606","https://openalex.org/W2041928877","https://openalex.org/W2049177827","https://openalex.org/W2065383440","https://openalex.org/W2069697210","https://openalex.org/W2070430508","https://openalex.org/W2074917656","https://openalex.org/W2076829842","https://openalex.org/W2080283002","https://openalex.org/W2093358477","https://openalex.org/W2095659203","https://openalex.org/W2107494372","https://openalex.org/W2120876740","https://openalex.org/W2123871098","https://openalex.org/W2133735014","https://openalex.org/W2158907191","https://openalex.org/W2333559992","https://openalex.org/W2473059737","https://openalex.org/W2486292461","https://openalex.org/W2486919360","https://openalex.org/W4236632459"],"related_works":["https://openalex.org/W3131922696","https://openalex.org/W2033468445","https://openalex.org/W1518096930","https://openalex.org/W3191967975","https://openalex.org/W2167187187","https://openalex.org/W2093863472","https://openalex.org/W2921374550","https://openalex.org/W4324027757","https://openalex.org/W2034885217","https://openalex.org/W2241787527"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
