{"id":"https://openalex.org/W2157001292","doi":"https://doi.org/10.1137/130927632","title":"An Approach to Nonlinear Viscoelasticity via Metric Gradient Flows","display_name":"An Approach to Nonlinear Viscoelasticity via Metric Gradient Flows","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2157001292","doi":"https://doi.org/10.1137/130927632","mag":"2157001292"},"language":"en","primary_location":{"id":"doi:10.1137/130927632","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130927632","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5052253534","display_name":"Alexander Mielke","orcid":"https://orcid.org/0000-0002-4583-3888"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alexander Mielke","raw_affiliation_strings":["Weierstra\u00df-Institut f\u00fcr Angewandte Analysis und Stochastik, Berlin 10117, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstra\u00df-Institut f\u00fcr Angewandte Analysis und Stochastik, Berlin 10117, Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061841111","display_name":"Christoph Ortner","orcid":"https://orcid.org/0000-0003-1498-8120"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Christoph Ortner","raw_affiliation_strings":["Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015399687","display_name":"Yasemin \u015eeng\u00fcl","orcid":"https://orcid.org/0000-0001-5923-3173"},"institutions":[{"id":"https://openalex.org/I44925452","display_name":"\u00d6zye\u011fin University","ror":"https://ror.org/01jjhfr75","country_code":"TR","type":"education","lineage":["https://openalex.org/I44925452"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Yasemin \u015eeng\u00fcl","raw_affiliation_strings":["Department of Natural and Mathematical Sciences, Ozyegin University, Istanbul 34794, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Natural and Mathematical Sciences, Ozyegin University, Istanbul 34794, Turkey","institution_ids":["https://openalex.org/I44925452"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7516,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.7316792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"46","issue":"2","first_page":"1317","last_page":"1347"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9952999949455261,"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":0.9952999949455261,"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/T12331","display_name":"Hereditary Neurological Disorders","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10379","display_name":"Cellular Mechanics and Interactions","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8266393542289734},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7187949419021606},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6679946780204773},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.598594069480896},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5969692468643188},{"id":"https://openalex.org/keywords/viscoelasticity","display_name":"Viscoelasticity","score":0.5875207185745239},{"id":"https://openalex.org/keywords/quasistatic-process","display_name":"Quasistatic process","score":0.5623558163642883},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5622854232788086},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.4694468677043915},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.44580283761024475},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.42674359679222107},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4193497896194458},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4159572422504425}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8266393542289734},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7187949419021606},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6679946780204773},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.598594069480896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5969692468643188},{"id":"https://openalex.org/C186541917","wikidata":"https://www.wikidata.org/wiki/Q910483","display_name":"Viscoelasticity","level":2,"score":0.5875207185745239},{"id":"https://openalex.org/C4708273","wikidata":"https://www.wikidata.org/wiki/Q900222","display_name":"Quasistatic process","level":2,"score":0.5623558163642883},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5622854232788086},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.4694468677043915},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44580283761024475},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.42674359679222107},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4193497896194458},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4159572422504425},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130927632","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130927632","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:eresearch.ozyegin.edu.tr:10679/746","is_oa":false,"landing_page_url":"http://hdl.handle.net/10679/746","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:https://orca.cardiff.ac.uk:145147","is_oa":false,"landing_page_url":"https://orca.cardiff.ac.uk/id/eprint/145147/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6135727698","display_name":null,"funder_award_id":"EP/E035027/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7602615794","display_name":null,"funder_award_id":"EP/D048400/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W157435084","https://openalex.org/W600787515","https://openalex.org/W1508861003","https://openalex.org/W1522579744","https://openalex.org/W1819883502","https://openalex.org/W1967879633","https://openalex.org/W1968878463","https://openalex.org/W2005116062","https://openalex.org/W2021089528","https://openalex.org/W2025774025","https://openalex.org/W2040671407","https://openalex.org/W2042401506","https://openalex.org/W2045069146","https://openalex.org/W2048623669","https://openalex.org/W2049368513","https://openalex.org/W2055086354","https://openalex.org/W2076806198","https://openalex.org/W2088703872","https://openalex.org/W2090896589","https://openalex.org/W2105340951","https://openalex.org/W2126066275","https://openalex.org/W2127143540","https://openalex.org/W2152517544","https://openalex.org/W2154639756","https://openalex.org/W2566073323","https://openalex.org/W2574852304","https://openalex.org/W3037446528","https://openalex.org/W3102850966"],"related_works":["https://openalex.org/W1983575846","https://openalex.org/W3167145102","https://openalex.org/W180211107","https://openalex.org/W1986781141","https://openalex.org/W3213441739","https://openalex.org/W4319792403","https://openalex.org/W1980174723","https://openalex.org/W2092244978","https://openalex.org/W2024955095","https://openalex.org/W2348351659"],"abstract_inverted_index":{"We":[0,78],"formulate":[1],"quasistatic":[2],"nonlinear":[3,17],"finite-strain":[4],"viscoelasticity":[5],"of":[6,36,53,58,64,75,97,100,107],"rate":[7],"type":[8],"as":[9],"a":[10,90,104,125],"gradient":[11,101],"system.":[12],"Our":[13],"focus":[14],"is":[15,82],"on":[16,27],"dissipation":[18,47],"functionals":[19],"and":[20,30,115],"distances":[21,48,108],"that":[22,31,80],"are":[23,116],"related":[24],"to":[25,118,120],"metrics":[26],"weak":[28],"diffeomorphisms":[29],"ensure":[32],"time-dependent":[33],"frame":[34],"indifference":[35],"the":[37,41,51,54,59,62,85,95,121],"viscoelastic":[38],"stress.":[39],"In":[40],"multidimensional":[42],"case":[43,87],"we":[44,109],"discuss":[45],"which":[46],"allow":[49],"for":[50],"solution":[52],"time-incremental":[55],"problem.":[56],"Because":[57],"missing":[60],"compactness":[61],"limit":[63,123],"vanishing":[65],"timesteps":[66],"can":[67],"be":[68],"obtained":[69],"only":[70],"by":[71,88],"proving":[72],"some":[73],"kind":[74],"strong":[76],"convergence.":[77],"show":[79],"this":[81],"possible":[83],"in":[84,94,124],"one-dimensional":[86],"using":[89],"suitably":[91],"generalized":[92],"convexity":[93,99],"sense":[96],"geodesic":[98],"flows.":[102],"For":[103],"general":[105],"class":[106],"derive":[110],"discrete":[111],"evolutionary":[112],"variational":[113],"inequalities":[114],"able":[117],"pass":[119],"time-continuous":[122],"specific":[126],"case.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
