{"id":"https://openalex.org/W4390092032","doi":"https://doi.org/10.48550/arxiv.2312.12776","title":"Computational homogenization of phase-field fracture","display_name":"Computational homogenization of phase-field fracture","publication_year":2023,"publication_date":"2023-12-20","ids":{"openalex":"https://openalex.org/W4390092032","doi":"https://doi.org/10.48550/arxiv.2312.12776"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2312.12776","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.12776","pdf_url":"https://arxiv.org/pdf/2312.12776","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2312.12776","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Schmidt, Felix","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Schmidt, Felix","raw_affiliation_strings":["Chair of Computational Mechanics , University of Siegen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Computational Mechanics , University of Siegen , Germany","institution_ids":["https://openalex.org/I206895457"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016134556","display_name":"S. Schu\u00df","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schu\u00df, Stefan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073579156","display_name":"Christian Hesch","orcid":"https://orcid.org/0000-0002-4614-2202","observed_orcids":["https://orcid.org/0000-0002-4614-2202"]},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hesch, Christian","raw_affiliation_strings":["Chair of Computational Mechanics , University of Siegen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Computational Mechanics , University of Siegen , Germany","institution_ids":["https://openalex.org/I206895457"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9789999723434448,"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/T10514","display_name":"Numerical methods in engineering","score":0.9789999723434448,"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":0.012299999594688416,"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/T11558","display_name":"Composite Material Mechanics","score":0.0015999999595806003,"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/phase-field-fracture","display_name":"phase-field fracture","score":0.9950000047683716},{"id":"https://openalex.org/keywords/two-scale-model","display_name":"two-scale modeling","score":0.7379999756813049},{"id":"https://openalex.org/keywords/thermodynamic-consistency","display_name":"thermodynamic consistency","score":0.9129999876022339},{"id":"https://openalex.org/keywords/anisotropic-damage","display_name":"anisotropic damage","score":0.9100000262260437},{"id":"https://openalex.org/keywords/macrofractures","display_name":"macrofractures","score":0.6240000128746033},{"id":"https://openalex.org/keywords/newton-raphson-linearization","display_name":"Newton-Raphson linearization","score":0.7549999952316284}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.9282733201980591},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.7904996871948242},{"id":"https://openalex.org/C2780568864","wikidata":"https://www.wikidata.org/wiki/Q1640482","display_name":"Phase field models","level":3,"score":0.6163546442985535},{"id":"https://openalex.org/C43369102","wikidata":"https://www.wikidata.org/wiki/Q2307625","display_name":"Fracture (geology)","level":2,"score":0.5812394618988037},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.5574761629104614},{"id":"https://openalex.org/C166955791","wikidata":"https://www.wikidata.org/wiki/Q629579","display_name":"Macro","level":2,"score":0.5007433891296387},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4397139847278595},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4340866506099701},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.39692920446395874},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.36185282468795776},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.29623299837112427},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2160320281982422},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.07618626952171326},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2312.12776","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.12776","pdf_url":"https://arxiv.org/pdf/2312.12776","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2312.12776","doi":"https://doi.org/10.48550/arxiv.2312.12776","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2312.12776","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2312.12776","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.12776","pdf_url":"https://arxiv.org/pdf/2312.12776","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390092032.pdf","grobid_xml":"https://content.openalex.org/works/W4390092032.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3131317940","https://openalex.org/W3131183298","https://openalex.org/W4388505701","https://openalex.org/W4393435360","https://openalex.org/W6999339774","https://openalex.org/W4411407747","https://openalex.org/W4210354786","https://openalex.org/W2892256426","https://openalex.org/W7166524044","https://openalex.org/W2144562394"],"abstract_inverted_index":{"In":[0,17],"this":[1],"contribution":[2],"we":[3,19],"investigate":[4],"the":[5,36,40,55,58,61,91,98,106],"application":[6],"of":[7,42,100],"phase-field":[8,63],"fracture":[9,69],"models":[10,102],"on":[11,23,35,54],"non-linear":[12],"multiscale":[13],"computational":[14],"homogenization":[15],"schemes.":[16],"particular,":[18],"introduce":[20],"different":[21,111],"phase-fields":[22,77],"a":[24,29,81,86],"two-scale":[25],"problem":[26],"and":[27],"develop":[28],"thermodynamically":[30],"consistent":[31,88],"model.":[32],"This":[33],"allows":[34,65],"one":[37],"hand":[38],"for":[39,90],"prediction":[41],"local":[43,74],"micro-fracture":[44],"patterns,":[45],"which":[46],"effectively":[47],"acts":[48],"as":[49,103,105],"an":[50],"anisotropic":[51],"damage":[52],"model":[53,64],"macroscale.":[56],"On":[57],"other":[59],"and,":[60],"macro-fracture":[62],"to":[66,73],"predict":[67],"complex":[68],"pattern":[70],"with":[71],"regard":[72],"microstructures.":[75],"Both":[76],"are":[78,108],"introduced":[79],"in":[80,110],"common":[82],"framework,":[83],"such":[84],"that":[85],"joint":[87],"linearization":[89],"Newton-Raphson":[92],"iteration":[93],"can":[94],"be":[95],"developed.":[96],"Finally,":[97],"limits":[99],"both":[101],"well":[104],"applicability":[107],"shown":[109],"numerical":[112],"examples.":[113]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2023-12-22T00:00:00"}
