{"id":"https://openalex.org/W2142523732","doi":"https://doi.org/10.1137/040607113","title":"A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues I: A General Formulation","display_name":"A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues I: A General Formulation","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2142523732","doi":"https://doi.org/10.1137/040607113","mag":"2142523732"},"language":"en","primary_location":{"id":"doi:10.1137/040607113","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607113","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","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/A5031055873","display_name":"Robyn P. Araujo","orcid":"https://orcid.org/0000-0002-3360-2214"},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Robyn P. Araujo","raw_affiliation_strings":["School of Mathematical Sciences, Queensland University of Technology, PO Box 2434 Brisbane, QLD 4001 Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queensland University of Technology, PO Box 2434 Brisbane, QLD 4001 Australia","institution_ids":["https://openalex.org/I160993911"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007539676","display_name":"D. L. S. McElwain","orcid":"https://orcid.org/0000-0002-7046-0251"},"institutions":[{"id":"https://openalex.org/I160993911","display_name":"Queensland University of Technology","ror":"https://ror.org/03pnv4752","country_code":"AU","type":"education","lineage":["https://openalex.org/I160993911"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"D. L. Sean McElwain","raw_affiliation_strings":["School of Mathematical Sciences, Queensland University of Technology, PO Box 2434 Brisbane, QLD 4001 Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queensland University of Technology, PO Box 2434 Brisbane, QLD 4001 Australia","institution_ids":["https://openalex.org/I160993911"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007539676"],"corresponding_institution_ids":["https://openalex.org/I160993911"],"apc_list":null,"apc_paid":null,"fwci":5.1197,"has_fulltext":false,"cited_by_count":79,"citation_normalized_percentile":{"value":0.95470805,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"65","issue":"4","first_page":"1261","last_page":"1284"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10379","display_name":"Cellular Mechanics and Interactions","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12085","display_name":"Collagen: Extraction and Characterization","score":0.9653000235557556,"subfield":{"id":"https://openalex.org/subfields/2502","display_name":"Biomaterials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mixture-theory","display_name":"Mixture theory","score":0.7988897562026978},{"id":"https://openalex.org/keywords/constitutive-equation","display_name":"Constitutive equation","score":0.7092734575271606},{"id":"https://openalex.org/keywords/inviscid-flow","display_name":"Inviscid flow","score":0.6630926728248596},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.4866641163825989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45323821902275085},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.41405385732650757},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4066615402698517},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3811325430870056},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.3650202453136444},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.33272209763526917},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.30911150574684143},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.21251055598258972}],"concepts":[{"id":"https://openalex.org/C2779736610","wikidata":"https://www.wikidata.org/wiki/Q6884140","display_name":"Mixture theory","level":3,"score":0.7988897562026978},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.7092734575271606},{"id":"https://openalex.org/C86252789","wikidata":"https://www.wikidata.org/wiki/Q2247765","display_name":"Inviscid flow","level":2,"score":0.6630926728248596},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4866641163825989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45323821902275085},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.41405385732650757},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4066615402698517},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3811325430870056},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.3650202453136444},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.33272209763526917},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30911150574684143},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.21251055598258972},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040607113","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607113","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.qut.edu.au:10258","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402607","display_name":"QUT ePrints (Queensland University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I160993911","host_organization_name":"Queensland University of Technology","host_organization_lineage":["https://openalex.org/I160993911"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"Contribution to Journal"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W122478729","https://openalex.org/W624910771","https://openalex.org/W1201922470","https://openalex.org/W1516879629","https://openalex.org/W1518050517","https://openalex.org/W1536348985","https://openalex.org/W1550439086","https://openalex.org/W1559736351","https://openalex.org/W1562251907","https://openalex.org/W1602259421","https://openalex.org/W1751852575","https://openalex.org/W1831674169","https://openalex.org/W1964042993","https://openalex.org/W1969176455","https://openalex.org/W1974158461","https://openalex.org/W1979169277","https://openalex.org/W1980440152","https://openalex.org/W1982147183","https://openalex.org/W1984581162","https://openalex.org/W1985153456","https://openalex.org/W2002011993","https://openalex.org/W2009073108","https://openalex.org/W2022575635","https://openalex.org/W2023880682","https://openalex.org/W2026691590","https://openalex.org/W2032725433","https://openalex.org/W2043967411","https://openalex.org/W2047677763","https://openalex.org/W2050624061","https://openalex.org/W2060489052","https://openalex.org/W2060694416","https://openalex.org/W2068037235","https://openalex.org/W2076230738","https://openalex.org/W2103209526","https://openalex.org/W2105607430","https://openalex.org/W2139262266","https://openalex.org/W2153807301","https://openalex.org/W2889747651","https://openalex.org/W4237997615","https://openalex.org/W4240837102","https://openalex.org/W4249313646","https://openalex.org/W4253538687","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1486213812","https://openalex.org/W2963995572","https://openalex.org/W2804509140","https://openalex.org/W1644877668","https://openalex.org/W1602020813","https://openalex.org/W3186153824","https://openalex.org/W2475486436","https://openalex.org/W1967490897","https://openalex.org/W2041718222","https://openalex.org/W2657349028"],"abstract_inverted_index":{"In":[0,134],"this":[1,81],"paper":[2],"a":[3,23,28,77,140,148,177,207,211,215],"theoretical":[4],"framework":[5,173],"for":[6,69,73,202],"the":[7,18,41,46,74,94,103,113,122,125,132,136,153,163,168,172,185,203],"study":[8],"of":[9,20,48,97,106,139,155,167,180,187,196,206,214],"residual":[10,52],"stresses":[11],"in":[12,50,124,128],"growing":[13],"tissues":[14],"is":[15,112,147,199],"presented":[16,68,174],"using":[17],"theory":[19],"mixtures.":[21],"Such":[22],"formulation":[24],"must":[25],"necessarily":[26],"be":[27],"solid-multiphase":[29,141,208],"model,":[30,209],"comprising":[31],"at":[32],"least":[33],"one":[34],"phase":[35],"with":[36,162],"solid":[37,169,217],"characteristics,":[38],"owing":[39],"to":[40,93,115,130,189],"fundamental":[42],"role":[43],"played":[44],"by":[45],"incompatibility":[47],"strains":[49],"generating":[51],"stresses.":[53],"Since":[54],"biological":[55,145],"growth":[56,146],"involves":[57],"mass":[58,110,157],"exchange":[59,111,158],"between":[60,121],"cellular":[61],"and":[62,72,218],"extracellular":[63],"phases,":[64],"field":[65],"equations":[66,85,198],"are":[67,86],"individual":[70],"phases":[71],"mixture":[75,213],"as":[76],"whole":[78],"which":[79,143,151,183],"incorporate":[80],"phenomenon.":[82],"Appropriate":[83],"constitutive":[84,119,149],"then":[87,200],"deduced":[88],"from":[89],"first":[90],"principles,":[91],"appealing":[92],"second":[95],"law":[96],"thermodynamics.":[98],"The":[99],"analysis":[100],"shows":[101],"that":[102],"distinguishing":[104],"feature":[105],"multiphase":[107],"models":[108,182],"involving":[109],"necessity":[114],"propose":[116],"an":[117,219],"additional":[118],"postulate":[120,150],"variables":[123],"mass-balance":[126],"equation":[127],"order":[129],"close":[131],"model.":[133],"particular,":[135],"defining":[137],"characteristic":[138],"model":[142],"describes":[144],"relates":[152],"process":[154],"interphase":[156],"(cell":[159],"proliferation/cell":[160],"death)":[161],"expansion":[164],"or":[165],"contraction":[166],"phase.":[170],"Thus,":[171],"here":[175],"represents":[176],"new":[178],"class":[179],"mathematical":[181],"extends":[184],"concepts":[186],"poroelasticity":[188],"accommodate":[190],"continuous":[191],"volumetric":[192],"growth.":[193],"A":[194],"set":[195],"modelling":[197],"proposed":[201],"simplest":[204],"case":[205],"being":[210],"biphasic":[212],"linear-elastic":[216],"inviscid":[220],"fluid.":[221]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}