{"id":"https://openalex.org/W7225429175","doi":"https://doi.org/10.46223/hcmcoujs.acs.en.16.2.91.2026","title":"Stochastics upscaling in multiscale mechanics and reduced model for fracture","display_name":"Stochastics upscaling in multiscale mechanics and reduced model for fracture","publication_year":2026,"publication_date":"2026-11-01","ids":{"openalex":"https://openalex.org/W7225429175","doi":"https://doi.org/10.46223/hcmcoujs.acs.en.16.2.91.2026"},"language":"en","primary_location":{"id":"doi:10.46223/hcmcoujs.acs.en.16.2.91.2026","doi":"https://doi.org/10.46223/hcmcoujs.acs.en.16.2.91.2026","is_oa":true,"landing_page_url":"https://doi.org/10.46223/hcmcoujs.acs.en.16.2.91.2026","pdf_url":"https://journalofscience.acs.ou.edu.vn/index.php/acs/article/download/91/51","source":{"id":"https://openalex.org/S5407034265","display_name":"HCMCOU Journal of Science \u2013 Advances in Computational Structures","issn_l":"2815-6218","issn":["2815-6218","2815-6226"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":"https://openalex.org/I4210096063","host_organization_name":"Ho Chi Minh City Open University","host_organization_lineage":["https://openalex.org/I4210096063"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"HCMCOU Journal of Science - Advances in Computational Structures","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://journalofscience.acs.ou.edu.vn/index.php/acs/article/download/91/51","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073642194","display_name":"Adnan Ibrahimbegovi\u0107","orcid":"https://orcid.org/0000-0002-6502-0198","observed_orcids":["https://orcid.org/0000-0002-6502-0198"]},"institutions":[{"id":"https://openalex.org/I102516824","display_name":"Universit\u00e9 de Technologie de Compi\u00e8gne","ror":"https://ror.org/04y5kwa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I102516824"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Adnan Ibrahimbegovic","raw_affiliation_strings":["Universit\u00e9 de Technologie Compi\u00e8gne - Alliance Sorbonne Universit\u00e9"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Technologie Compi\u00e8gne - Alliance Sorbonne Universit\u00e9","institution_ids":["https://openalex.org/I102516824","https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073642194"],"corresponding_institution_ids":["https://openalex.org/I102516824","https://openalex.org/I39804081"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.625,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.625,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.2632000148296356,"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":0.030799999833106995,"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/multiscale-mechanics","display_name":"multiscale mechanics","score":0.9810000061988831},{"id":"https://openalex.org/keywords/fracture","display_name":"fracture","score":0.6209999918937683},{"id":"https://openalex.org/keywords/material-heterogeneity","display_name":"material heterogeneity","score":0.7390000224113464},{"id":"https://openalex.org/keywords/epistemic-uncertainty","display_name":"epistemic uncertainty","score":0.8659999966621399},{"id":"https://openalex.org/keywords/bayesian-updating","display_name":"Bayesian updating","score":0.925000011920929},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.9760000109672546},{"id":"https://openalex.org/keywords/homogenization","display_name":"homogenization","score":0.7400000095367432},{"id":"https://openalex.org/keywords/concrete","display_name":"concrete","score":0.8399999737739563},{"id":"https://openalex.org/keywords/scaling-laws","display_name":"scaling laws","score":0.6129999756813049},{"id":"https://openalex.org/keywords/random-fields","display_name":"random fields","score":0.6620000004768372}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.7124999761581421},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5238000154495239},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.512499988079071},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.5078999996185303},{"id":"https://openalex.org/C43369102","wikidata":"https://www.wikidata.org/wiki/Q2307625","display_name":"Fracture (geology)","level":2,"score":0.49709999561309814},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4616999924182892},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.45159998536109924},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42910000681877136},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.42800000309944153},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.3783999979496002},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.3546999990940094},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3434000015258789},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3361000120639801},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.3061000108718872},{"id":"https://openalex.org/C59085676","wikidata":"https://www.wikidata.org/wiki/Q957852","display_name":"Fracture mechanics","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C52421305","wikidata":"https://www.wikidata.org/wiki/Q1151499","display_name":"Particle filter","level":3,"score":0.2809000015258789},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C91716921","wikidata":"https://www.wikidata.org/wiki/Q1289366","display_name":"Scale parameter","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2621000111103058},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.26170000433921814},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25529998540878296}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.46223/hcmcoujs.acs.en.16.2.91.2026","doi":"https://doi.org/10.46223/hcmcoujs.acs.en.16.2.91.2026","is_oa":true,"landing_page_url":"https://doi.org/10.46223/hcmcoujs.acs.en.16.2.91.2026","pdf_url":"https://journalofscience.acs.ou.edu.vn/index.php/acs/article/download/91/51","source":{"id":"https://openalex.org/S5407034265","display_name":"HCMCOU Journal of Science \u2013 Advances in Computational Structures","issn_l":"2815-6218","issn":["2815-6218","2815-6226"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":"https://openalex.org/I4210096063","host_organization_name":"Ho Chi Minh City Open University","host_organization_lineage":["https://openalex.org/I4210096063"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"HCMCOU Journal of Science - Advances in Computational Structures","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.46223/hcmcoujs.acs.en.16.2.91.2026","doi":"https://doi.org/10.46223/hcmcoujs.acs.en.16.2.91.2026","is_oa":true,"landing_page_url":"https://doi.org/10.46223/hcmcoujs.acs.en.16.2.91.2026","pdf_url":"https://journalofscience.acs.ou.edu.vn/index.php/acs/article/download/91/51","source":{"id":"https://openalex.org/S5407034265","display_name":"HCMCOU Journal of Science \u2013 Advances in Computational Structures","issn_l":"2815-6218","issn":["2815-6218","2815-6226"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":"https://openalex.org/I4210096063","host_organization_name":"Ho Chi Minh City Open University","host_organization_lineage":["https://openalex.org/I4210096063"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"HCMCOU Journal of Science - Advances in Computational Structures","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320315323","display_name":"Technology Agency of the Czech Republic","ror":null},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225429175.pdf","grobid_xml":"https://content.openalex.org/works/W7225429175.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1512208174","https://openalex.org/W1550160156","https://openalex.org/W1608370595","https://openalex.org/W1920004557","https://openalex.org/W1935801564","https://openalex.org/W1968263654","https://openalex.org/W1969575045","https://openalex.org/W1974509726","https://openalex.org/W1976374868","https://openalex.org/W1996991329","https://openalex.org/W1998806251","https://openalex.org/W2002242880","https://openalex.org/W2008356811","https://openalex.org/W2009866282","https://openalex.org/W2018159038","https://openalex.org/W2031574620","https://openalex.org/W2033675870","https://openalex.org/W2044246955","https://openalex.org/W2056760934","https://openalex.org/W2060174126","https://openalex.org/W2064332562","https://openalex.org/W2070064241","https://openalex.org/W2102125272","https://openalex.org/W2105934661","https://openalex.org/W2130416410","https://openalex.org/W2165834163","https://openalex.org/W2168527745","https://openalex.org/W2211895605","https://openalex.org/W2224896188","https://openalex.org/W2465685852","https://openalex.org/W2503500554","https://openalex.org/W2508655381","https://openalex.org/W2763985728","https://openalex.org/W2801733251","https://openalex.org/W2808876779","https://openalex.org/W2885423467","https://openalex.org/W2946235086","https://openalex.org/W2954474284","https://openalex.org/W3117256701","https://openalex.org/W3217167116","https://openalex.org/W4256038730","https://openalex.org/W4281732543","https://openalex.org/W4301163938","https://openalex.org/W4408109355"],"related_works":["https://openalex.org/W4281732543","https://openalex.org/W4410709247","https://openalex.org/W4298849053","https://openalex.org/W7135430636","https://openalex.org/W2792244774","https://openalex.org/W4416953350","https://openalex.org/W26161694","https://openalex.org/W1987264787","https://openalex.org/W2943949709","https://openalex.org/W3117256701"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"the":[3,9,37,68,77,90,93,111,119,135,147,154,164,168,198],"idea":[4],"of":[5,11,54,156,201],"stochastic":[6,31,50,165,199],"upscaling,":[7],"with":[8,76,81,149],"aim":[10],"clarifying":[12],"how":[13],"to":[14,35,46,118,158,181,187],"handle":[15],"uncertainty":[16],"at":[17,126,146],"each":[18],"scale":[19,177],"by":[20,41],"describing":[21],"mechanical":[22],"system":[23,193],"parameters":[24,194],"through":[25],"random":[26],"quantities":[27],"or":[28,160],"spatially":[29],"varying":[30],"fields.":[32],"We":[33],"intend":[34],"demonstrate":[36],"essential":[38,174],"role":[39],"played":[40],"small-scale":[42],"material":[43],"heterogeneities":[44],"and":[45],"formulate":[47],"a":[48,82,98,127,142,150],"new":[49],"upscaling":[51,166],"framework,":[52],"capable":[53],"capturing":[55],"their":[56],"influence":[57],"on":[58],"macroscopic":[59],"fracture":[60,133,157],"behavior.":[61],"The":[62],"results":[63],"for":[64,85,89,105,176],"concrete":[65],"show":[66],"that":[67,110],"Bayesian":[69,106],"updating":[70],"method":[71,80],"produces":[72],"posterior":[73,115,144],"distributions":[74],"consistent":[75],"deterministic":[78],"homogenization":[79,184],"Gaussian":[83],"distribution":[84,94,145,152],"elastic":[86],"parameters,":[87,92,134],"whereas,":[88],"inelastic":[91],"is":[95,139,172],"no":[96],"longer":[97],"simple":[99],"Gaussian.":[100],"Comparing":[101],"two":[102],"proposed":[103,169],"methods":[104],"inference,":[107],"we":[108],"find":[109],"Gauss-Markov-Kalman":[112],"filter":[113],"achieves":[114],"estimates":[116],"equivalent":[117],"Markov":[120],"chain":[121],"Monte":[122],"Carlo":[123],"method,":[124],"but":[125],"much":[128],"lower":[129],"computational":[130],"cost.":[131],"For":[132],"micro-scale":[136],"spatial":[137],"variation":[138],"preserved":[140],"as":[141,195,197],"non-normal":[143],"macro-scale":[148],"probability":[151],"reflecting":[153],"sensitivity":[155],"initial":[159],"induced":[161],"defects.":[162],"Accordingly,":[163],"in":[167,185,192],"multiscale":[170],"framework":[171],"an":[173],"component":[175],"laws,":[178],"allowing":[179],"one":[180],"move":[182],"beyond":[183],"order":[186],"properly":[188],"incorporate":[189],"epistemic":[190],"uncertainties":[191],"well":[196],"character":[200],"fracture.":[202]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-07T00:00:00"}