{"id":"https://openalex.org/W2891875627","doi":"https://doi.org/10.1121/2.0000844","title":"Internal-variable modeling of solids with slow dynamics: Wave propagation and resonance simulations","display_name":"Internal-variable modeling of solids with slow dynamics: Wave propagation and resonance simulations","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2891875627","doi":"https://doi.org/10.1121/2.0000844","mag":"2891875627"},"language":"en","primary_location":{"id":"doi:10.1121/2.0000844","is_oa":true,"landing_page_url":"https://doi.org/10.1121/2.0000844","pdf_url":"https://asa.scitation.org/doi/pdf/10.1121/2.0000844","source":{"id":"https://openalex.org/S4306523472","display_name":"Proceedings of meetings on acoustics","issn_l":"1939-800X","issn":["1939-800X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320226","host_organization_name":"Acoustical Society of America","host_organization_lineage":["https://openalex.org/P4310320226"],"host_organization_lineage_names":["Acoustical Society of America"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of Meetings on Acoustics","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://asa.scitation.org/doi/pdf/10.1121/2.0000844","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012185705","display_name":"Harold Berjamin","orcid":"https://orcid.org/0000-0001-6637-8485"},"institutions":[{"id":"https://openalex.org/I4210142724","display_name":"Centrale Marseille","ror":"https://ror.org/040baw385","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142724"]},{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Harold Berjamin","raw_affiliation_strings":["Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13453, FRANCE;","Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13453, FRANCE"],"affiliations":[{"raw_affiliation_string":"Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13453, FRANCE;","institution_ids":["https://openalex.org/I4210142724"]},{"raw_affiliation_string":"Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13453, FRANCE","institution_ids":["https://openalex.org/I4210142724","https://openalex.org/I21491767"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070189720","display_name":"Guillaume Chiavassa","orcid":null},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210142724","display_name":"Centrale Marseille","ror":"https://ror.org/040baw385","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Guillaume Chiavassa","raw_affiliation_strings":["Centrale Marseille, CNRS, Aix-Marseille University, M2P2 UMR 7340, Marseille, 13453, FRANCE;","Centrale Marseille, CNRS, Aix-Marseille University, M2P2 UMR 7340, Marseille, 13453, FRANCE"],"affiliations":[{"raw_affiliation_string":"Centrale Marseille, CNRS, Aix-Marseille University, M2P2 UMR 7340, Marseille, 13453, FRANCE;","institution_ids":["https://openalex.org/I4210142724"]},{"raw_affiliation_string":"Centrale Marseille, CNRS, Aix-Marseille University, M2P2 UMR 7340, Marseille, 13453, FRANCE","institution_ids":["https://openalex.org/I4210142724","https://openalex.org/I21491767"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009864697","display_name":"Nicolas Favrie","orcid":"https://orcid.org/0000-0003-3788-2927"},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210143353","display_name":"Institut Universitaire des Syst\u00e8mes Thermiques Industriels","ror":"https://ror.org/04bgbbh33","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210095849","https://openalex.org/I4210143353"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Nicolas Favrie","raw_affiliation_strings":["Aix-Marseille University, UMR CNRS 7343, IUSTI; Polytech Marseille, Marseille, 13451, FRANCE;","Polytech Marseille, Marseille, 13451, FRANCE","Aix-Marseille University, UMR CNRS 7343, IUSTI"],"affiliations":[{"raw_affiliation_string":"Aix-Marseille University, UMR CNRS 7343, IUSTI; Polytech Marseille, Marseille, 13451, FRANCE;","institution_ids":["https://openalex.org/I21491767"]},{"raw_affiliation_string":"Polytech Marseille, Marseille, 13451, FRANCE","institution_ids":[]},{"raw_affiliation_string":"Aix-Marseille University, UMR CNRS 7343, IUSTI","institution_ids":["https://openalex.org/I21491767","https://openalex.org/I4210143353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022008525","display_name":"Bruno Lombard","orcid":"https://orcid.org/0000-0002-5648-2737"},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210142724","display_name":"Centrale Marseille","ror":"https://ror.org/040baw385","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Bruno Lombard","raw_affiliation_strings":["Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13451, FRANCE; [email\u00a0protected];","[email\u00a0protected]","Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13451, FRANCE"],"affiliations":[{"raw_affiliation_string":"Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13451, FRANCE; [email\u00a0protected];","institution_ids":["https://openalex.org/I4210142724"]},{"raw_affiliation_string":"[email\u00a0protected]","institution_ids":[]},{"raw_affiliation_string":"Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13451, FRANCE","institution_ids":["https://openalex.org/I4210142724","https://openalex.org/I21491767"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000228910","display_name":"Emmanuelle Sarrouy","orcid":"https://orcid.org/0000-0002-0236-708X"},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210142724","display_name":"Centrale Marseille","ror":"https://ror.org/040baw385","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Emmanuelle Sarrouy","raw_affiliation_strings":["Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13451, FRANCE; [email\u00a0protected];","Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13451, FRANCE","[email\u00a0protected]"],"affiliations":[{"raw_affiliation_string":"Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13451, FRANCE; [email\u00a0protected];","institution_ids":["https://openalex.org/I4210142724"]},{"raw_affiliation_string":"Aix-Marseille University, CNRS, Centrale Marseille, LMA, Marseille, 13451, FRANCE","institution_ids":["https://openalex.org/I4210142724","https://openalex.org/I21491767"]},{"raw_affiliation_string":"[email\u00a0protected]","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5000228910","https://openalex.org/A5009864697","https://openalex.org/A5012185705","https://openalex.org/A5022008525","https://openalex.org/A5070189720"],"corresponding_institution_ids":["https://openalex.org/I21491767","https://openalex.org/I4210142724","https://openalex.org/I4210143353"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10939472,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"022001","last_page":"022001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","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"}},"topics":[{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","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"}},{"id":"https://openalex.org/T12603","display_name":"NMR spectroscopy and applications","score":0.9843000173568726,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11874","display_name":"Structural Response to Dynamic Loads","score":0.9825000166893005,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/harmonic-balance","display_name":"Harmonic balance","score":0.7183738946914673},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6869519948959351},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.5138828754425049},{"id":"https://openalex.org/keywords/constitutive-equation","display_name":"Constitutive equation","score":0.49655014276504517},{"id":"https://openalex.org/keywords/viscoelasticity","display_name":"Viscoelasticity","score":0.47579893469810486},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4506634473800659},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.45063063502311707},{"id":"https://openalex.org/keywords/resonance","display_name":"Resonance (particle physics)","score":0.4279130697250366},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.42563343048095703},{"id":"https://openalex.org/keywords/time-domain","display_name":"Time domain","score":0.42333346605300903},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.36965590715408325},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33442598581314087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2855840027332306},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21287432312965393},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.13920587301254272},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.13488882780075073}],"concepts":[{"id":"https://openalex.org/C121758426","wikidata":"https://www.wikidata.org/wiki/Q5659248","display_name":"Harmonic balance","level":3,"score":0.7183738946914673},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6869519948959351},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5138828754425049},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.49655014276504517},{"id":"https://openalex.org/C186541917","wikidata":"https://www.wikidata.org/wiki/Q910483","display_name":"Viscoelasticity","level":2,"score":0.47579893469810486},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4506634473800659},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.45063063502311707},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.4279130697250366},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.42563343048095703},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.42333346605300903},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.36965590715408325},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33442598581314087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2855840027332306},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21287432312965393},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.13920587301254272},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.13488882780075073},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1121/2.0000844","is_oa":true,"landing_page_url":"https://doi.org/10.1121/2.0000844","pdf_url":"https://asa.scitation.org/doi/pdf/10.1121/2.0000844","source":{"id":"https://openalex.org/S4306523472","display_name":"Proceedings of meetings on acoustics","issn_l":"1939-800X","issn":["1939-800X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320226","host_organization_name":"Acoustical Society of America","host_organization_lineage":["https://openalex.org/P4310320226"],"host_organization_lineage_names":["Acoustical Society of America"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of Meetings on Acoustics","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1121/2.0000844","is_oa":true,"landing_page_url":"https://doi.org/10.1121/2.0000844","pdf_url":"https://asa.scitation.org/doi/pdf/10.1121/2.0000844","source":{"id":"https://openalex.org/S4306523472","display_name":"Proceedings of meetings on acoustics","issn_l":"1939-800X","issn":["1939-800X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320226","host_organization_name":"Acoustical Society of America","host_organization_lineage":["https://openalex.org/P4310320226"],"host_organization_lineage_names":["Acoustical Society of America"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of Meetings on Acoustics","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1153485594","display_name":null,"funder_award_id":"A*MIDEX","funder_id":"https://openalex.org/F4320309911","funder_display_name":"Aix-Marseille Universit\u00e9"},{"id":"https://openalex.org/G4973929103","display_name":null,"funder_award_id":"funding","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"},{"id":"https://openalex.org/G7758152977","display_name":null,"funder_award_id":"support","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"}],"funders":[{"id":"https://openalex.org/F4320309911","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2891875627.pdf","grobid_xml":"https://content.openalex.org/works/W2891875627.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2002342109","https://openalex.org/W2023871291","https://openalex.org/W2081742229","https://openalex.org/W2086414472","https://openalex.org/W2151867868","https://openalex.org/W2611779140","https://openalex.org/W2790535682"],"related_works":["https://openalex.org/W4221057967","https://openalex.org/W4243019676","https://openalex.org/W2517352629","https://openalex.org/W2783562378","https://openalex.org/W4293192718","https://openalex.org/W2045876794","https://openalex.org/W2089309364","https://openalex.org/W2354516437","https://openalex.org/W3162315667","https://openalex.org/W2393848258"],"abstract_inverted_index":{"Rocks":[0],"and":[1,41,88,103],"concrete":[2],"are":[3],"known":[4],"to":[5,80,108,122],"soften":[6],"under":[7],"a":[8,35],"dynamic":[9],"loading,":[10],"i.e.":[11],"the":[12,39,46,109],"speed":[13],"of":[14,27,34,51,65],"sound":[15],"diminishes":[16],"with":[17,120],"forcing":[18],"amplitudes.":[19],"To":[20],"reproduce":[21,81],"this":[22],"behavior,":[23],"an":[24,42],"internal-variable":[25],"model":[26],"continuum":[28],"is":[29,32,54,69,78,106,114],"proposed.":[30],"It":[31],"composed":[33],"constitutive":[36],"law":[37],"for":[38,45,56,116],"stress":[40],"evolution":[43],"equation":[44],"internal":[47,60],"variable.":[48],"Nonlinear":[49,83],"viscoelasticity":[50],"Zener":[52],"type":[53],"accounted":[55],"by":[57],"using":[58,72],"additional":[59],"variables.":[61],"The":[62,75],"proposed":[63],"system":[64],"partial":[66],"differential":[67],"equations":[68],"solved":[70],"numerically":[71],"finite-volume":[73],"methods.":[74],"numerical":[76,104],"tool":[77],"used":[79],"qualitatively":[82],"Resonance":[84],"Ultrasound":[85],"Spectroscopy":[86],"(NRUS)":[87],"Dynamic":[89],"Acoustoelastic":[90],"Testing":[91],"(DAET)":[92],"experiments.":[93,124],"A":[94],"frequency-domain":[95],"approach":[96,113],"based":[97],"on":[98],"finite":[99],"elements,":[100],"harmonic":[101],"balance":[102],"continuation":[105],"compared":[107],"time-domain":[110],"method.":[111],"This":[112],"promising":[115],"upcoming":[117],"experimental":[118],"validations":[119],"respect":[121],"resonance":[123]},"counts_by_year":[],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}
