{"id":"https://openalex.org/W4297039766","doi":"https://doi.org/10.1061/(asce)mt.1943-5533.0004366","title":"Determining with High Accuracy the Relaxation Modulus and Creep Compliance of Asphaltic Materials in the Form of Sums of Exponential Functions from Mathematical Master Curves of Dynamic Modulus","display_name":"Determining with High Accuracy the Relaxation Modulus and Creep Compliance of Asphaltic Materials in the Form of Sums of Exponential Functions from Mathematical Master Curves of Dynamic Modulus","publication_year":2022,"publication_date":"2022-06-27","ids":{"openalex":"https://openalex.org/W4297039766","doi":"https://doi.org/10.1061/(asce)mt.1943-5533.0004366"},"language":"en","primary_location":{"id":"doi:10.1061/(asce)mt.1943-5533.0004366","doi":"https://doi.org/10.1061/(asce)mt.1943-5533.0004366","is_oa":false,"landing_page_url":"https://doi.org/10.1061/(asce)mt.1943-5533.0004366","pdf_url":null,"source":{"id":"https://openalex.org/S111427844","display_name":"Journal of Materials in Civil Engineering","issn_l":"0899-1561","issn":["0899-1561","1943-5533"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315747","host_organization_name":"American Society of Civil Engineers","host_organization_lineage":["https://openalex.org/P4310315747"],"host_organization_lineage_names":["American Society of Civil Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Materials in Civil Engineering","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034555347","display_name":"Thanh-Nhan Phan","orcid":"https://orcid.org/0000-0001-8807-6867","observed_orcids":["https://orcid.org/0000-0001-8807-6867"]},"institutions":[{"id":"https://openalex.org/I4210148201","display_name":"Ho Chi Minh City University of Technology and Engineering","ror":"https://ror.org/05hzn5427","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210148201"]},{"id":"https://openalex.org/I4391012539","display_name":"Thu Dau Mot University","ror":"https://ror.org/010y5b925","country_code":"VN","type":"education","lineage":["https://openalex.org/I4391012539"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Thanh-Nhan Phan","raw_affiliation_strings":["Lecturer, Faculty of Architecture, Thu Dau Mot Univ., 06 Tran Van On St., Phu Hoa Ward, Thu Dau Mot City, Binh Duong Province 75000, Vietnam; Faculty of Civil Engineering, Ho Chi Minh City Univ. of Technology and Education, 01 Vo Van Ngan St., Linh Chieu Ward, Thu Duc City, Ho Chi Minh City 70000, Vietnam","Lecturer, Faculty of Architecture, Thu Dau Mot Univ., 06 Tran Van On St., Phu Hoa Ward, Thu Dau Mot City, Binh Duong Province 75000, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lecturer, Faculty of Architecture, Thu Dau Mot Univ., 06 Tran Van On St., Phu Hoa Ward, Thu Dau Mot City, Binh Duong Province 75000, Vietnam; Faculty of Civil Engineering, Ho Chi Minh City Univ. of Technology and Education, 01 Vo Van Ngan St., Linh Chieu Ward, Thu Duc City, Ho Chi Minh City 70000, Vietnam","institution_ids":["https://openalex.org/I4210148201","https://openalex.org/I4391012539"]},{"raw_affiliation_string":"Lecturer, Faculty of Architecture, Thu Dau Mot Univ., 06 Tran Van On St., Phu Hoa Ward, Thu Dau Mot City, Binh Duong Province 75000, Vietnam","institution_ids":["https://openalex.org/I4391012539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032712770","display_name":"Duy\u2010Liem Nguyen","orcid":"https://orcid.org/0000-0001-7176-1518","observed_orcids":["https://orcid.org/0000-0001-7176-1518"]},"institutions":[{"id":"https://openalex.org/I4210148201","display_name":"Ho Chi Minh City University of Technology and Engineering","ror":"https://ror.org/05hzn5427","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210148201"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Duy-Liem Nguyen","raw_affiliation_strings":["Lecturer, Faculty of Civil Engineering, Ho Chi Minh City Univ. of Technology and Education, 01 Vo Van Ngan St., Linh Chieu Ward, Thu Duc City, Ho Chi Minh City 70000, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lecturer, Faculty of Civil Engineering, Ho Chi Minh City Univ. of Technology and Education, 01 Vo Van Ngan St., Linh Chieu Ward, Thu Duc City, Ho Chi Minh City 70000, Vietnam","institution_ids":["https://openalex.org/I4210148201"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074819366","display_name":"Tan-Van Vu","orcid":"https://orcid.org/0000-0001-8319-2703","observed_orcids":["https://orcid.org/0000-0001-8319-2703"]},"institutions":[{"id":"https://openalex.org/I3132362326","display_name":"Ho Chi Minh City University of Architecture","ror":"https://ror.org/02tyvzz27","country_code":"VN","type":"education","lineage":["https://openalex.org/I3132362326"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Tan-Van Vu","raw_affiliation_strings":["Associate Professor, Dept. of Civil Engineering, Univ. of Architecture Ho Chi Minh City, 196 Pasteur St., Vo Thi Sau Ward, District 3, Ho Chi Minh City 70000, Vietnam. ORCID:","Associate Professor, Dept. of Civil Engineering, Univ. of Architecture Ho Chi Minh City, 196 Pasteur St., Vo Thi Sau Ward, District 3, Ho Chi Minh City 70000, Vietnam. ORCID: https://orcid.org/0000-0001-8319-2703"],"raw_orcid":"https://orcid.org/0000-0001-8319-2703","affiliations":[{"raw_affiliation_string":"Associate Professor, Dept. of Civil Engineering, Univ. of Architecture Ho Chi Minh City, 196 Pasteur St., Vo Thi Sau Ward, District 3, Ho Chi Minh City 70000, Vietnam. ORCID:","institution_ids":["https://openalex.org/I3132362326"]},{"raw_affiliation_string":"Associate Professor, Dept. of Civil Engineering, Univ. of Architecture Ho Chi Minh City, 196 Pasteur St., Vo Thi Sau Ward, District 3, Ho Chi Minh City 70000, Vietnam. ORCID: https://orcid.org/0000-0001-8319-2703","institution_ids":["https://openalex.org/I3132362326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028908001","display_name":"Vu-Tu Tran","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210148201","display_name":"Ho Chi Minh City University of Technology and Engineering","ror":"https://ror.org/05hzn5427","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210148201"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Vu-Tu Tran","raw_affiliation_strings":["Lecturer, Faculty of Civil Engineering, Ho Chi Minh City Univ. of Technology and Education, 01 Vo Van Ngan St., Linh Chieu Ward, Thu Duc City, Ho Chi Minh City 70000, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lecturer, Faculty of Civil Engineering, Ho Chi Minh City Univ. of Technology and Education, 01 Vo Van Ngan St., Linh Chieu Ward, Thu Duc City, Ho Chi Minh City 70000, Vietnam","institution_ids":["https://openalex.org/I4210148201"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101398457","display_name":"H. T. Tai Nguyen","orcid":"https://orcid.org/0000-0003-3257-3535","observed_orcids":["https://orcid.org/0000-0003-3257-3535"]},"institutions":[{"id":"https://openalex.org/I4210148201","display_name":"Ho Chi Minh City University of Technology and Engineering","ror":"https://ror.org/05hzn5427","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210148201"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"H. T. Tai Nguyen","raw_affiliation_strings":["Lecturer, Faculty of Civil Engineering, Ho Chi Minh City Univ. of Technology and Education, 01 Vo Van Ngan St., Linh Chieu Ward, Thu Duc City, Ho Chi Minh City 70000, Vietnam (corresponding author). ORCID: ","Lecturer, Faculty of Civil Engineering, Ho Chi Minh City Univ. of Technology and Education, 01 Vo Van Ngan St., Linh Chieu Ward, Thu Duc City, Ho Chi Minh City 70000, Vietnam. ORCID: https://orcid.org/0000-0003-3257-3535"],"raw_orcid":"https://orcid.org/0000-0003-3257-3535","affiliations":[{"raw_affiliation_string":"Lecturer, Faculty of Civil Engineering, Ho Chi Minh City Univ. of Technology and Education, 01 Vo Van Ngan St., Linh Chieu Ward, Thu Duc City, Ho Chi Minh City 70000, Vietnam (corresponding author). ORCID: ","institution_ids":["https://openalex.org/I4210148201"]},{"raw_affiliation_string":"Lecturer, Faculty of Civil Engineering, Ho Chi Minh City Univ. of Technology and Education, 01 Vo Van Ngan St., Linh Chieu Ward, Thu Duc City, Ho Chi Minh City 70000, Vietnam. ORCID: https://orcid.org/0000-0003-3257-3535","institution_ids":["https://openalex.org/I4210148201"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078469487","display_name":"Mai Lan Nguyen","orcid":"https://orcid.org/0000-0001-8966-5209","observed_orcids":["https://orcid.org/0000-0001-8966-5209"]},"institutions":[{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I2800365227","https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mai Lan Nguyen","raw_affiliation_strings":["Senior Researcher, Dept. of Materials and Structures, Gustave Eiffel Univ., Bouguenais 44344, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Senior Researcher, Dept. of Materials and Structures, Gustave Eiffel Univ., Bouguenais 44344, France","institution_ids":["https://openalex.org/I4210154111"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101398457"],"corresponding_institution_ids":["https://openalex.org/I4210148201"],"apc_list":null,"apc_paid":null,"fwci":0.5292,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.57001271,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"34","issue":"9","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10264","display_name":"Asphalt Pavement Performance Evaluation","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10264","display_name":"Asphalt Pavement Performance Evaluation","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/bitumen","display_name":"bitumen","score":0.7540000081062317},{"id":"https://openalex.org/keywords/relaxation-modulus","display_name":"relaxation modulus","score":0.9860000014305115},{"id":"https://openalex.org/keywords/creep-compliance","display_name":"creep compliance","score":1.0},{"id":"https://openalex.org/keywords/master-curve","display_name":"master curve","score":0.722000002861023},{"id":"https://openalex.org/keywords/dynamic-modulus","display_name":"dynamic modulus","score":0.9729999899864197},{"id":"https://openalex.org/keywords/phase-angle","display_name":"phase angle","score":0.8379999995231628},{"id":"https://openalex.org/keywords/kramers-kronig-relations","display_name":"Kramers-Kronig relations","score":0.9210000038146973},{"id":"https://openalex.org/keywords/causality","display_name":"causality","score":0.8849999904632568},{"id":"https://openalex.org/keywords/linear-viscoelasticity","display_name":"linear viscoelasticity","score":0.9900000095367432},{"id":"https://openalex.org/keywords/storage-modulus","display_name":"storage modulus","score":0.847000002861023},{"id":"https://openalex.org/keywords/compliance","display_name":"compliance","score":0.4009999930858612},{"id":"https://openalex.org/keywords/closed-form-expressions","display_name":"closed-form expressions","score":0.5600000023841858}],"concepts":[{"id":"https://openalex.org/C186541917","wikidata":"https://www.wikidata.org/wiki/Q910483","display_name":"Viscoelasticity","level":2,"score":0.7275422215461731},{"id":"https://openalex.org/C193867417","wikidata":"https://www.wikidata.org/wiki/Q6889814","display_name":"Modulus","level":2,"score":0.6704873442649841},{"id":"https://openalex.org/C149912024","wikidata":"https://www.wikidata.org/wiki/Q462188","display_name":"Creep","level":2,"score":0.6438484191894531},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6313384175300598},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6078523397445679},{"id":"https://openalex.org/C170222088","wikidata":"https://www.wikidata.org/wiki/Q2059855","display_name":"Phase angle (astronomy)","level":2,"score":0.5367409586906433},{"id":"https://openalex.org/C191204318","wikidata":"https://www.wikidata.org/wiki/Q246574","display_name":"Dynamic modulus","level":4,"score":0.5367324352264404},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.44819843769073486},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.41454237699508667},{"id":"https://openalex.org/C21036866","wikidata":"https://www.wikidata.org/wiki/Q181767","display_name":"Stress (linguistics)","level":2,"score":0.41393980383872986},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3825277090072632},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37695905566215515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3733908534049988},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32448139786720276},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.24229001998901367},{"id":"https://openalex.org/C7055690","wikidata":"https://www.wikidata.org/wiki/Q900639","display_name":"Dynamic mechanical analysis","level":3,"score":0.21924951672554016},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16469573974609375},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.12621572613716125},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C521977710","wikidata":"https://www.wikidata.org/wiki/Q81163","display_name":"Polymer","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1061/(asce)mt.1943-5533.0004366","doi":"https://doi.org/10.1061/(asce)mt.1943-5533.0004366","is_oa":false,"landing_page_url":"https://doi.org/10.1061/(asce)mt.1943-5533.0004366","pdf_url":null,"source":{"id":"https://openalex.org/S111427844","display_name":"Journal of Materials in Civil Engineering","issn_l":"0899-1561","issn":["0899-1561","1943-5533"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315747","host_organization_name":"American Society of Civil Engineers","host_organization_lineage":["https://openalex.org/P4310315747"],"host_organization_lineage_names":["American Society of Civil Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Materials in Civil Engineering","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04498532v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-04498532","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Materials in Civil Engineering, 2022, 34 (9), &#x27E8;10.1061/(ASCE)MT.1943-5533.0004366&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1972020031","https://openalex.org/W1977480877","https://openalex.org/W1981800077","https://openalex.org/W1990104843","https://openalex.org/W1995584133","https://openalex.org/W2023329384","https://openalex.org/W2030882384","https://openalex.org/W2032637233","https://openalex.org/W2035126287","https://openalex.org/W2037346624","https://openalex.org/W2054775321","https://openalex.org/W2057181974","https://openalex.org/W2063232232","https://openalex.org/W2326943206","https://openalex.org/W2501456448","https://openalex.org/W2506867931","https://openalex.org/W2525597528","https://openalex.org/W2730174091","https://openalex.org/W2782875863","https://openalex.org/W2783569200","https://openalex.org/W2903252454","https://openalex.org/W3043317052","https://openalex.org/W3080344761","https://openalex.org/W3096808815","https://openalex.org/W3106252540","https://openalex.org/W3125247376","https://openalex.org/W3147798398","https://openalex.org/W4231460384","https://openalex.org/W4246525044"],"related_works":["https://openalex.org/W4386484205","https://openalex.org/W4206269454","https://openalex.org/W2094714348","https://openalex.org/W3125247376","https://openalex.org/W4296836639","https://openalex.org/W4387796231","https://openalex.org/W2087675494","https://openalex.org/W1985820837","https://openalex.org/W971041813","https://openalex.org/W2587650957"],"abstract_inverted_index":{"According":[0],"to":[1,17,27,40,66,144,190,209],"the":[2,6,30,41,44,48,55,68,78,83,88,99,103,107,121,126,132,138,146,150,154,160,179,183,191,196,202,214,229,236],"physical":[3],"causality":[4,45],"principle,":[5],"two":[7,24],"components":[8],"of":[9,43,50,73,90,92,102,128,182,195,239],"complex":[10],"modulus":[11,32,80,162,198],"are":[12],"not":[13],"independent":[14],"yet":[15],"interrelated":[16],"each":[18],"other":[19,56],"via":[20],"Kramers-Kronig":[21],"relationships.":[22],"Using":[23],"mathematical":[25,64],"functions":[26,94],"predict":[28,67],"simultaneously":[29],"dynamic":[31],"(DM)":[33],"and":[34,123,156,163,167,185,199,216],"phase":[35],"angle":[36],"(PA)":[37],"generally":[38],"leads":[39],"violation":[42],"principle.":[46],"Therefore,":[47],"calculation":[49],"one":[51,57],"component":[52],"based":[53,130,148],"on":[54,131,149],"is":[58,96],"a":[59,113,175],"vital":[60],"task":[61],"for":[62,98,116,220],"using":[63,174],"models":[65],"linear":[69],"viscoelastic":[70],"(LVE)":[71],"behavior":[72],"asphaltic":[74],"materials.":[75],"In":[76],"addition,":[77],"relaxation":[79],"(RM)":[81],"or":[82],"creep":[84],"compliance":[85,164],"(CC)":[86],"in":[87,106,125,223,228],"form":[89,127,193],"sums":[91],"exponential":[93],"(SEFs)":[95],"necessary":[97],"efficient":[100],"resolution":[101],"stress\u2013strain":[104],"relationship":[105,152],"time":[108,230],"domain.":[109,231],"This":[110],"paper":[111],"presented":[112],"novel":[114],"method":[115,225],"calculating":[117,251],"with":[118,169,211],"high":[119,170,212],"accuracy":[120,171,213],"RM":[122,184,215],"CC":[124,186,217],"SEFs":[129,173,219],"input":[133],"DM":[134],"master":[135],"curve.":[136],"First,":[137],"midpoint":[139],"integration":[140],"scheme":[141],"was":[142,205],"used":[143,206],"calculate":[145],"PA":[147,155],"exact":[151],"between":[153],"DM.":[157],"After":[158],"that,":[159],"storage":[161,197],"were":[165,187,244],"computed":[166,243],"decomposed":[168],"into":[172,218],"special":[176,192,203],"technique.":[177],"Then,":[178],"closed-form":[180],"formula":[181],"derived":[188],"thanks":[189],"function":[194],"compliance.":[200],"Finally,":[201],"technique":[204],"once":[207],"again":[208],"decompose":[210],"possible":[221],"uses":[222],"finite-element":[224],"(FEM)":[226],"analysis":[227],"The":[232],"results":[233],"showed":[234],"that":[235],"relative":[237],"errors":[238],"all":[240,250],"LVE":[241],"properties":[242],"lower":[245],"than":[246],"0.1":[247],"percent":[248],"at":[249],"points.":[252]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-10-27T15:51:10.671819","created_date":"2022-09-26T00:00:00"}
