{"id":"https://openalex.org/W3138691578","doi":"https://doi.org/10.3390/s21062061","title":"Experimental and Numerical Investigation of the Micro-Crack Damage in Elastic Solids by Two-Way Collinear Mixing Method","display_name":"Experimental and Numerical Investigation of the Micro-Crack Damage in Elastic Solids by Two-Way Collinear Mixing Method","publication_year":2021,"publication_date":"2021-03-15","ids":{"openalex":"https://openalex.org/W3138691578","doi":"https://doi.org/10.3390/s21062061","mag":"3138691578","pmid":"https://pubmed.ncbi.nlm.nih.gov/33804180"},"language":"en","primary_location":{"id":"doi:10.3390/s21062061","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s21062061","pdf_url":"https://www.mdpi.com/1424-8220/21/6/2061/pdf?version=1615818533","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Sensors","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1424-8220/21/6/2061/pdf?version=1615818533","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049463614","display_name":"Hong Jun Liu","orcid":"https://orcid.org/0000-0002-3027-3435"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongjun Liu","raw_affiliation_strings":["College of Aerospace Engineering, Chongqing University, Chongqing 400044, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Aerospace Engineering, Chongqing University, Chongqing 400044, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110790801","display_name":"Youxuan Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Youxuan Zhao","raw_affiliation_strings":["Chongqing Key Laboratory of Heterogeneous Material Mechanics, Chongqing University, Chongqing 400044, China","College of Aerospace Engineering, Chongqing University, Chongqing 400044, China"],"raw_orcid":"https://orcid.org/0000-0001-7412-8216","affiliations":[{"raw_affiliation_string":"Chongqing Key Laboratory of Heterogeneous Material Mechanics, Chongqing University, Chongqing 400044, China","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"College of Aerospace Engineering, Chongqing University, Chongqing 400044, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100399276","display_name":"Han Zhang","orcid":"https://orcid.org/0000-0002-0166-1973"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210099069","display_name":"Institute of Acoustics","ror":"https://ror.org/00v8rqv75","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210099069"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Han Zhang","raw_affiliation_strings":["Key Laboratory of Noise and Vibration, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Noise and Vibration, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210099069","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062730384","display_name":"Mingxi Deng","orcid":"https://orcid.org/0000-0001-9522-4039"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingxi Deng","raw_affiliation_strings":["College of Aerospace Engineering, Chongqing University, Chongqing 400044, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Aerospace Engineering, Chongqing University, Chongqing 400044, China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100783980","display_name":"Ning Hu","orcid":"https://orcid.org/0000-0002-6444-8467"},"institutions":[{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ning Hu","raw_affiliation_strings":["National Engineering Research Center for Technological Innovation Method and Tool, Hebei University of Technology, Tianjin 300401, China","School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China","State Key Laboratory of Reliability and Intelligence Electrical Equipment, Hebei University of Technology, Tianjin 300401, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Engineering Research Center for Technological Innovation Method and Tool, Hebei University of Technology, Tianjin 300401, China","institution_ids":["https://openalex.org/I184843921"]},{"raw_affiliation_string":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China","institution_ids":["https://openalex.org/I184843921"]},{"raw_affiliation_string":"State Key Laboratory of Reliability and Intelligence Electrical Equipment, Hebei University of Technology, Tianjin 300401, China","institution_ids":["https://openalex.org/I184843921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032098234","display_name":"Xiaoyang Bi","orcid":"https://orcid.org/0000-0003-4542-7465"},"institutions":[{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoyang Bi","raw_affiliation_strings":["School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China","institution_ids":["https://openalex.org/I184843921"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100783980","https://openalex.org/A5110790801"],"corresponding_institution_ids":["https://openalex.org/I158842170","https://openalex.org/I184843921"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2598},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2598},"fwci":1.307,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.75653893,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"21","issue":"6","first_page":"2061","last_page":"2061"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":1.0,"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/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":1.0,"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/T10396","display_name":"Fatigue and fracture mechanics","score":0.9991999864578247,"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":0.9969000220298767,"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/materials-science","display_name":"Materials science","score":0.7714273929595947},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.6771969795227051},{"id":"https://openalex.org/keywords/transverse-plane","display_name":"Transverse plane","score":0.6463873982429504},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5470621585845947},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.4897196590900421},{"id":"https://openalex.org/keywords/aluminium","display_name":"Aluminium","score":0.48075148463249207},{"id":"https://openalex.org/keywords/crack-closure","display_name":"Crack closure","score":0.4343467354774475},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.4305415153503418},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.29206281900405884},{"id":"https://openalex.org/keywords/fracture-mechanics","display_name":"Fracture mechanics","score":0.2650092840194702},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14458826184272766},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06096762418746948}],"concepts":[{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.7714273929595947},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.6771969795227051},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.6463873982429504},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5470621585845947},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.4897196590900421},{"id":"https://openalex.org/C513153333","wikidata":"https://www.wikidata.org/wiki/Q663","display_name":"Aluminium","level":2,"score":0.48075148463249207},{"id":"https://openalex.org/C75512024","wikidata":"https://www.wikidata.org/wiki/Q17009280","display_name":"Crack closure","level":3,"score":0.4343467354774475},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4305415153503418},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.29206281900405884},{"id":"https://openalex.org/C59085676","wikidata":"https://www.wikidata.org/wiki/Q957852","display_name":"Fracture mechanics","level":2,"score":0.2650092840194702},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14458826184272766},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06096762418746948},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/s21062061","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s21062061","pdf_url":"https://www.mdpi.com/1424-8220/21/6/2061/pdf?version=1615818533","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Sensors","raw_type":"journal-article"},{"id":"pmid:33804180","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33804180","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:d2fa423c694a400fb1da3da81d464732","is_oa":true,"landing_page_url":"https://doaj.org/article/d2fa423c694a400fb1da3da81d464732","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors, Vol 21, Iss 6, p 2061 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1424-8220/21/6/2061/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/s21062061","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Sensors; Volume 21; Issue 6; Pages: 2061","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8001703","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8001703","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Sensors (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/s21062061","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s21062061","pdf_url":"https://www.mdpi.com/1424-8220/21/6/2061/pdf?version=1615818533","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Sensors","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4781460794","display_name":null,"funder_award_id":"A2020202002","funder_id":"https://openalex.org/F4320322163","funder_display_name":"Natural Science Foundation of Hebei Province"},{"id":"https://openalex.org/G4824724236","display_name":null,"funder_award_id":"S20ZDF077","funder_id":"https://openalex.org/F4320323993","funder_display_name":"Natural Science Foundation of Tianjin City"},{"id":"https://openalex.org/G8448965962","display_name":null,"funder_award_id":"11632004 and 11604033","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323993","display_name":"Natural Science Foundation of Tianjin City","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3138691578.pdf","grobid_xml":"https://content.openalex.org/works/W3138691578.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W93449779","https://openalex.org/W1257677611","https://openalex.org/W1610643741","https://openalex.org/W1978822752","https://openalex.org/W1981796192","https://openalex.org/W1985804075","https://openalex.org/W1988948086","https://openalex.org/W1995234526","https://openalex.org/W1997392718","https://openalex.org/W1997484429","https://openalex.org/W2010270487","https://openalex.org/W2018472921","https://openalex.org/W2018656896","https://openalex.org/W2023050816","https://openalex.org/W2035784549","https://openalex.org/W2052294079","https://openalex.org/W2055419787","https://openalex.org/W2058566700","https://openalex.org/W2061227630","https://openalex.org/W2076892885","https://openalex.org/W2079042924","https://openalex.org/W2082688085","https://openalex.org/W2084371178","https://openalex.org/W2087753248","https://openalex.org/W2088737486","https://openalex.org/W2094600035","https://openalex.org/W2098722929","https://openalex.org/W2152152092","https://openalex.org/W2159466891","https://openalex.org/W2165125925","https://openalex.org/W2173982804","https://openalex.org/W2460336151","https://openalex.org/W2539614516","https://openalex.org/W2594297304","https://openalex.org/W2606462227","https://openalex.org/W2606576256","https://openalex.org/W2739065604","https://openalex.org/W2746045581","https://openalex.org/W2758934971","https://openalex.org/W2791797779","https://openalex.org/W2793505602","https://openalex.org/W2809166720","https://openalex.org/W2810932317","https://openalex.org/W2875706684","https://openalex.org/W2883376601","https://openalex.org/W2894267034","https://openalex.org/W2897530122","https://openalex.org/W2898187925","https://openalex.org/W2947058242","https://openalex.org/W2983767919","https://openalex.org/W2985009452","https://openalex.org/W2994747445","https://openalex.org/W3025738665","https://openalex.org/W3034095635","https://openalex.org/W3042514095","https://openalex.org/W3046933498","https://openalex.org/W3049418860","https://openalex.org/W3092194065","https://openalex.org/W3105141904","https://openalex.org/W6682279616","https://openalex.org/W6753252439","https://openalex.org/W6785821518"],"related_works":["https://openalex.org/W4242396160","https://openalex.org/W4237955578","https://openalex.org/W2171564338","https://openalex.org/W2373038869","https://openalex.org/W2077266348","https://openalex.org/W2068809356","https://openalex.org/W2606567852","https://openalex.org/W2063409105","https://openalex.org/W2088584521","https://openalex.org/W2394366509"],"abstract_inverted_index":{"This":[0],"study":[1],"experimentally":[2],"and":[3,32,42,86],"numerically":[4],"investigated":[5],"the":[6,10,16,29,37,47,53,63,75,78,81,93,110,119,123],"nonlinear":[7],"behavior":[8],"of":[9,49,77,83,89],"resonant":[11,50,54,84],"bulk":[12],"waves":[13,34,51,85],"generated":[14,99],"by":[15,100,117],"two-way":[17,124],"collinear":[18,125],"mixing":[19,126],"method":[20],"in":[21,36,72,96],"5052":[22],"aluminum":[23],"alloy":[24],"with":[25,70],"micro-crack":[26,38,73,79,90,94,111],"damage.":[27],"When":[28],"primary":[30],"longitudinal":[31],"transverse":[33],"mixed":[35],"damage":[39,95,112],"region,":[40,80],"numerical":[41],"experimental":[43],"results":[44],"both":[45],"verified":[46],"generation":[48],"if":[52],"condition":[55],"\u03c9L/\u03c9T=2\u03ba/(\u03ba-1)":[56],"was":[57,104,107],"satisfied.":[58],"Meanwhile,":[59],"we":[60],"found":[61,108],"that":[62,109],"acoustic":[64],"nonlinearity":[65],"parameter":[66],"(ANP)":[67],"increases":[68,71],"monotonously":[69],"density,":[74],"size":[76],"frequency":[82],"friction":[87],"coefficient":[88],"surfaces.":[91],"Furthermore,":[92],"a":[97],"specimen":[98,120],"low-temperature":[101],"fatigue":[102],"experiment":[103],"employed.":[105],"It":[106],"region":[113],"can":[114],"be":[115],"located":[116],"scanning":[118],"based":[121],"on":[122],"method.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-14T08:27:34.040176","created_date":"2025-10-10T00:00:00"}
