{"id":"https://openalex.org/W7167664348","doi":"https://doi.org/10.3390/math14193566","title":"A Comparative Review of Fatigue Modeling Approaches in Metals: From Total-Life Methods to Fracture-Based Models","display_name":"A Comparative Review of Fatigue Modeling Approaches in Metals: From Total-Life Methods to Fracture-Based Models","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7167664348","doi":"https://doi.org/10.3390/math14193566"},"language":"en","primary_location":{"id":"doi:10.3390/math14193566","doi":"https://doi.org/10.3390/math14193566","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14193566","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/math14193566","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091111764","display_name":"L.A. Gon\u00e7alves","orcid":"https://orcid.org/0000-0001-6565-0416","observed_orcids":["https://orcid.org/0000-0001-6565-0416"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. A. Gon\u00e7alves Junior","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002180917","display_name":"Luc\u00eda Gratiela Barbu","orcid":"https://orcid.org/0000-0002-3542-4853","observed_orcids":["https://orcid.org/0000-0002-3542-4853"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. G. Barbu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049574844","display_name":"Sergio Jim\u00e9nez","orcid":"https://orcid.org/0000-0001-7982-2725","observed_orcids":["https://orcid.org/0000-0001-7982-2725"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Jim\u00e9nez","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7982-2725","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140255037","display_name":"A. Cornejo","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Cornejo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5048815053","display_name":"Sergio Oller","orcid":"https://orcid.org/0000-0002-5203-8903","observed_orcids":["https://orcid.org/0000-0002-5203-8903"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Oller","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35117568,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"19","first_page":"3566","last_page":"3566"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10396","display_name":"Fatigue and fracture mechanics","score":0.9951000213623047,"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/T10396","display_name":"Fatigue and fracture mechanics","score":0.9951000213623047,"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/T10514","display_name":"Numerical methods in engineering","score":0.002300000051036477,"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/T10219","display_name":"Mechanical Behavior of Composites","score":0.0010000000474974513,"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/fatigue-modeling","display_name":"fatigue modeling","score":0.9380000233650208},{"id":"https://openalex.org/keywords/metals","display_name":"metals","score":0.8960000276565552},{"id":"https://openalex.org/keywords/stress-life-approach","display_name":"stress-life approach","score":0.8389999866485596},{"id":"https://openalex.org/keywords/strain-life-approach","display_name":"strain-life approach","score":1.0},{"id":"https://openalex.org/keywords/fracture-mechanics","display_name":"fracture mechanics","score":0.8840000033378601},{"id":"https://openalex.org/keywords/continuum-damage-mechanics","display_name":"continuum damage mechanics","score":0.9980000257492065},{"id":"https://openalex.org/keywords/phase-field-theory","display_name":"phase field theory","score":0.906000018119812},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"extended finite element method","score":0.8740000128746033},{"id":"https://openalex.org/keywords/fatigue-life-prediction","display_name":"fatigue life prediction","score":0.781000018119812},{"id":"https://openalex.org/keywords/fatigue-failure","display_name":"fatigue failure","score":0.5149999856948853}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6467999815940857},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4357999861240387},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.3675999939441681},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.32600000500679016},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.3084999918937683},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.30320000648498535},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.2955000102519989},{"id":"https://openalex.org/C2985278600","wikidata":"https://www.wikidata.org/wiki/Q65051469","display_name":"Fatigue testing","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C43369102","wikidata":"https://www.wikidata.org/wiki/Q2307625","display_name":"Fracture (geology)","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.24070000648498535}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/math14193566","doi":"https://doi.org/10.3390/math14193566","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14193566","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"doi:10.20944/preprints202607.0270.v1","doi":"https://doi.org/10.20944/preprints202607.0270.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202607.0270.v1","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"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":"posted-content"},{"id":"pmh:oai:doaj.org/article:d551d0adcecc489883f85078c4f26d60","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/d551d0adcecc489883f85078c4f26d60","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Mathematics, Vol 14, Iss 19, p 3566 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math14193566","doi":"https://doi.org/10.3390/math14193566","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14193566","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6704136972","display_name":"TWINNING FOR EXCELLENCE IN TUBITAK ON THE FATIGUE SIMULATION OF ADDITIVE MANUFACTURED PARTS","funder_award_id":"101159809","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7355482924","display_name":"Fatigue modelling and fast testing methodologies to optimize part design and to boost lightweight materials deployment in chassis parts","funder_award_id":"101006844","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":173,"referenced_works":["https://openalex.org/W24262370","https://openalex.org/W73308757","https://openalex.org/W108690888","https://openalex.org/W171737220","https://openalex.org/W227729886","https://openalex.org/W1445910544","https://openalex.org/W1513751997","https://openalex.org/W1533827645","https://openalex.org/W1533983817","https://openalex.org/W1553390994","https://openalex.org/W1566694159","https://openalex.org/W1734040340","https://openalex.org/W1965169720","https://openalex.org/W1967070136","https://openalex.org/W1968427925","https://openalex.org/W1969591790","https://openalex.org/W1970499362","https://openalex.org/W1971941310","https://openalex.org/W1973469855","https://openalex.org/W1974516303","https://openalex.org/W1977188519","https://openalex.org/W1977671639","https://openalex.org/W1980915300","https://openalex.org/W1984903998","https://openalex.org/W1987576086","https://openalex.org/W1987895449","https://openalex.org/W1989624292","https://openalex.org/W1991658866","https://openalex.org/W1993664919","https://openalex.org/W1999791618","https://openalex.org/W2001012537","https://openalex.org/W2003000852","https://openalex.org/W2004491319","https://openalex.org/W2006078294","https://openalex.org/W2006829903","https://openalex.org/W2010884885","https://openalex.org/W2014200034","https://openalex.org/W2016623075","https://openalex.org/W2017290161","https://openalex.org/W2018481516","https://openalex.org/W2019729827","https://openalex.org/W2019825941","https://openalex.org/W2020923190","https://openalex.org/W2021041712","https://openalex.org/W2024557370","https://openalex.org/W2027019914","https://openalex.org/W2029274644","https://openalex.org/W2030117832","https://openalex.org/W2030509416","https://openalex.org/W2031796544","https://openalex.org/W2031942432","https://openalex.org/W2032057523","https://openalex.org/W2032391798","https://openalex.org/W2033882205","https://openalex.org/W2034374704","https://openalex.org/W2035818421","https://openalex.org/W2036136913","https://openalex.org/W2036247319","https://openalex.org/W2036667241","https://openalex.org/W2037600881","https://openalex.org/W2039198037","https://openalex.org/W2040099098","https://openalex.org/W2041697026","https://openalex.org/W2043784721","https://openalex.org/W2052815421","https://openalex.org/W2053715726","https://openalex.org/W2054595416","https://openalex.org/W2056515813","https://openalex.org/W2056868916","https://openalex.org/W2060012526","https://openalex.org/W2060248859","https://openalex.org/W2061473722","https://openalex.org/W2062054836","https://openalex.org/W2062462433","https://openalex.org/W2064800633","https://openalex.org/W2067480498","https://openalex.org/W2067873902","https://openalex.org/W2072086953","https://openalex.org/W2073974083","https://openalex.org/W2078997432","https://openalex.org/W2079682366","https://openalex.org/W2082616441","https://openalex.org/W2084464066","https://openalex.org/W2085999139","https://openalex.org/W2086645014","https://openalex.org/W2088893558","https://openalex.org/W2089057061","https://openalex.org/W2089624394","https://openalex.org/W2089679418","https://openalex.org/W2091896438","https://openalex.org/W2093256786","https://openalex.org/W2093712558","https://openalex.org/W2101996824","https://openalex.org/W2108498594","https://openalex.org/W2109209629","https://openalex.org/W2114207581","https://openalex.org/W2114487471","https://openalex.org/W2116434326","https://openalex.org/W2117496726","https://openalex.org/W2125276515","https://openalex.org/W2133799982","https://openalex.org/W2142596047","https://openalex.org/W2145572133","https://openalex.org/W2145580705","https://openalex.org/W2145995141","https://openalex.org/W2150697691","https://openalex.org/W2154410528","https://openalex.org/W2155280009","https://openalex.org/W2157258353","https://openalex.org/W2163442709","https://openalex.org/W2165834163","https://openalex.org/W2259805772","https://openalex.org/W2262652728","https://openalex.org/W2283363096","https://openalex.org/W2397262573","https://openalex.org/W2478347644","https://openalex.org/W2482939998","https://openalex.org/W2497025309","https://openalex.org/W2499374078","https://openalex.org/W2505515853","https://openalex.org/W2555415669","https://openalex.org/W2582712463","https://openalex.org/W2596953173","https://openalex.org/W2604947251","https://openalex.org/W2773128197","https://openalex.org/W2773515741","https://openalex.org/W2791201795","https://openalex.org/W2894089608","https://openalex.org/W2899766161","https://openalex.org/W2907785071","https://openalex.org/W2916750126","https://openalex.org/W2925431143","https://openalex.org/W2967472796","https://openalex.org/W2977462023","https://openalex.org/W2981549529","https://openalex.org/W2990820591","https://openalex.org/W3010191168","https://openalex.org/W3015525178","https://openalex.org/W3034658082","https://openalex.org/W3034773464","https://openalex.org/W3045486394","https://openalex.org/W3084200341","https://openalex.org/W3110585066","https://openalex.org/W3118286239","https://openalex.org/W3121371773","https://openalex.org/W3134025560","https://openalex.org/W3134875744","https://openalex.org/W3149474751","https://openalex.org/W3163149202","https://openalex.org/W3204151563","https://openalex.org/W3206441344","https://openalex.org/W3214140278","https://openalex.org/W4205934444","https://openalex.org/W4210361900","https://openalex.org/W4214545539","https://openalex.org/W4225582332","https://openalex.org/W4230777501","https://openalex.org/W4285603290","https://openalex.org/W4293859878","https://openalex.org/W4293874319","https://openalex.org/W4299993525","https://openalex.org/W4310726139","https://openalex.org/W4311970746","https://openalex.org/W4319073312","https://openalex.org/W4362560449","https://openalex.org/W4377694819","https://openalex.org/W4379184173","https://openalex.org/W4385757165","https://openalex.org/W4393219860","https://openalex.org/W4398162792","https://openalex.org/W4409915332","https://openalex.org/W4410106404","https://openalex.org/W4413759343"],"related_works":["https://openalex.org/W4409915332","https://openalex.org/W2524356231","https://openalex.org/W2141554164","https://openalex.org/W4249605216","https://openalex.org/W4381335758","https://openalex.org/W7214583208","https://openalex.org/W4417200554","https://openalex.org/W4385430397","https://openalex.org/W2363349243","https://openalex.org/W16334152"],"abstract_inverted_index":{"Fatigue":[0],"is":[1,20],"widely":[2],"recognized":[3],"as":[4,100],"one":[5],"of":[6,17,29,43,45,107,119],"the":[7,23,37,46,56,61,92,105],"primary":[8],"failure":[9,19],"mechanisms":[10],"affecting":[11],"metallic":[12],"structures.":[13],"Consequently,":[14],"reliable":[15],"prediction":[16,28],"fatigue-induced":[18],"essential":[21],"for":[22,50,104,130],"safe":[24],"design":[25],"and":[26,32,63,84,91,124],"lifetime":[27],"engineering":[30],"structures":[31],"components.":[33],"In":[34],"this":[35],"context,":[36],"present":[38],"work":[39],"provides":[40],"an":[41],"overview":[42],"some":[44],"main":[47],"approaches":[48,70,112],"employed":[49],"fatigue":[51,72],"modeling":[52],"in":[53,78,117],"metals.":[54],"First,":[55],"classical":[57],"total-life":[58],"methods,":[59],"namely":[60],"stress\u2013life":[62],"strain\u2013life":[64],"approaches,":[65],"are":[66,73,97,113,133],"reviewed.":[67],"Subsequently,":[68],"fracture-based":[69],"to":[71],"presented,":[74],"including":[75],"formulations":[76],"grounded":[77],"fracture":[79],"mechanics,":[80,83],"continuum":[81],"damage":[82],"phase-field":[85],"theory.":[86],"The":[87,110],"finite":[88,94],"element":[89,95],"method":[90,96],"extended":[93],"also":[98],"discussed":[99],"representative":[101],"numerical":[102],"frameworks":[103],"implementation":[106],"these":[108],"formulations.":[109],"reviewed":[111],"then":[114],"critically":[115],"compared":[116],"terms":[118],"their":[120],"applicability,":[121],"capabilities,":[122],"limitations":[123],"calibration":[125],"requirements.":[126],"Finally,":[127],"relevant":[128],"directions":[129],"future":[131],"research":[132],"identified.":[134]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-07-09T00:00:00"}