{"id":"https://openalex.org/W7213276604","doi":"https://doi.org/10.48550/arxiv.2609.13449","title":"MORTIS: Quadrature-compatible cofactor gauges and optimal material margins in finite elasticity","display_name":"MORTIS: Quadrature-compatible cofactor gauges and optimal material margins in finite elasticity","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7213276604","doi":"https://doi.org/10.48550/arxiv.2609.13449"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13449","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13449","pdf_url":"https://arxiv.org/pdf/2609.13449","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.13449","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147347748","display_name":"Yanlin Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Liu, Yanlin","raw_affiliation_strings":["The University of Melbourne"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Melbourne","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137701169","display_name":"Kaixiang Yao","orcid":"https://orcid.org/0009-0004-4096-5007","observed_orcids":["https://orcid.org/0009-0004-4096-5007"]},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yao, Kaixiang","raw_affiliation_strings":["Southern University of Science,Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Southern University of Science,Technology","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091518548","display_name":"Chao Huang","orcid":"https://orcid.org/0000-0002-2062-1512","observed_orcids":["https://orcid.org/0000-0002-2062-1512"]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huang, Chao","raw_affiliation_strings":["Shanghai Jiao Tong University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5151797488","display_name":"Yao Shen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shen, Yao","raw_affiliation_strings":["Shanghai Jiao Tong University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.961899995803833,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.961899995803833,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.029100000858306885,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.0026000000070780516,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-elasticity","display_name":"finite elasticity","score":0.7760000228881836},{"id":"https://openalex.org/keywords/tangent-stiffness","display_name":"tangent stiffness","score":0.375},{"id":"https://openalex.org/keywords/convex-loss-functions","display_name":"convex loss functions","score":0.4390000104904175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7750999927520752},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6377999782562256},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.5194000005722046},{"id":"https://openalex.org/C126530901","wikidata":"https://www.wikidata.org/wiki/Q432635","display_name":"Coercivity","level":2,"score":0.44780001044273376},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.42329999804496765},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4034000039100647},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.39730000495910645},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.39340001344680786},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.3659000098705292},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.352400004863739},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.34880000352859497},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.31130000948905945},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C119830904","wikidata":"https://www.wikidata.org/wiki/Q233220","display_name":"Second fundamental form","level":4,"score":0.27709999680519104},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.2531000077724457},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13449","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13449","pdf_url":"https://arxiv.org/pdf/2609.13449","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.13449","doi":"https://doi.org/10.48550/arxiv.2609.13449","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13449","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.13449","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13449","pdf_url":"https://arxiv.org/pdf/2609.13449","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213276604.pdf","grobid_xml":"https://content.openalex.org/works/W7213276604.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W74748254","https://openalex.org/W1545761024","https://openalex.org/W1969500188","https://openalex.org/W1978620595","https://openalex.org/W2006730584","https://openalex.org/W2007515850","https://openalex.org/W2019852530","https://openalex.org/W2020804487","https://openalex.org/W2039373590","https://openalex.org/W2044178072","https://openalex.org/W2048267518","https://openalex.org/W2081036239","https://openalex.org/W2087240734","https://openalex.org/W2088703872","https://openalex.org/W2121168715","https://openalex.org/W2170345902","https://openalex.org/W2265706702","https://openalex.org/W2912522929","https://openalex.org/W2963179762","https://openalex.org/W4286209657","https://openalex.org/W4375844751","https://openalex.org/W4381549509","https://openalex.org/W4392741283","https://openalex.org/W4405863607","https://openalex.org/W4414295469","https://openalex.org/W6968689014"],"related_works":["https://openalex.org/W7065875724","https://openalex.org/W3032438865","https://openalex.org/W2580342130","https://openalex.org/W2492596978","https://openalex.org/W1996664317","https://openalex.org/W7213371123","https://openalex.org/W2998508181","https://openalex.org/W2196658912","https://openalex.org/W2995877212","https://openalex.org/W2006290497"],"abstract_inverted_index":{"We":[0,32],"develop":[1],"a":[2,51,56,61,98,129,145,161,195],"discrete":[3],"design":[4],"theory":[5,203],"for":[6,39],"cofactor":[7],"reference":[8],"forms":[9,139],"that":[10],"preserve":[11],"the":[12,22,25,34,65,87,124,133,141],"complete":[13],"finite-element":[14],"elasticity":[15],"tangent.":[16],"A":[17,93,120],"fixed":[18],"continuous":[19],"potential":[20,37,90,150],"generates":[21],"coefficient,":[23],"while":[24,194],"variation":[26],"space":[27,76],"and":[28,47,77,106,137,170,178,204,213],"quadrature":[29,177],"determine":[30],"compatibility.":[31],"classify":[33],"exact":[35,154],"local":[36,207],"spaces":[38],"all-order":[40],"tensor":[41,158],"elements,":[42],"anisotropic":[43],"spaces,":[44],"cubic":[45],"serendipity":[46],"quadratic":[48],"tetrahedra.":[49],"At":[50],"stress-free":[52,162],"Mooney-Rivlin":[53],"state":[54],"with":[55,186],"common":[57],"positive":[58,115],"material-coefficient":[59],"sum,":[60],"convex":[62],"loss":[63],"expresses":[64],"attainable":[66],"quadrature-point":[67],"material":[68,209],"margin.":[69],"The":[70,202],"optimum":[71],"is":[72,83,91],"attained;":[73],"under":[74,111,173],"stated":[75,134],"sampling":[78],"assumptions,":[79],"its":[80],"ideal":[81],"value":[82],"attained":[84],"precisely":[85],"when":[86],"physical":[88,163],"identity":[89,122],"compatible.":[92],"conforming":[94],"fixed-candidate":[95],"example":[96],"proves":[97],"strict":[99],"margin":[100,131],"loss,":[101],"linear":[102],"in":[103,108,132,167],"curvature":[104],"amplitude":[105],"uniform":[107,166],"cell":[109,189],"size,":[110],"displacement":[112,171],"enrichment.":[113],"Explicit":[114],"candidates":[116],"accompany":[117],"this":[118],"restriction.":[119],"Gram":[121],"gives":[123],"sharp":[125],"constant-coefficient":[126],"defect":[127],"at":[128],"prescribed":[130],"norm.":[135],"Compatible":[136],"reference-defect-corrected":[138],"retain":[140],"original":[142],"tangent":[143],"through":[144],"deformation-independent":[146],"external-boundary":[147],"Hessian;":[148],"equal":[149,153],"traces":[151],"give":[152],"assembled":[155],"gauges.":[156],"Quadratic":[157],"geometry":[159],"admits":[160],"coercivity":[164,212],"bound":[165],"mesh":[168],"size":[169],"order":[172],"explicit":[174],"material,":[175],"shape,":[176],"boundary":[179],"assumptions.":[180],"Certified":[181],"curved":[182],"tetrahedral":[183],"shear":[184],"families":[185],"zero":[187],"recovered":[188],"pressure":[190],"establish":[191],"finite-deformation":[192],"regimes,":[193],"loaded":[196],"pressure-curvature":[197],"counterexample":[198],"identifies":[199],"their":[200],"limitation.":[201],"observations":[205],"distinguish":[206],"exactness,":[208],"certificates,":[210],"complete-reference":[211],"unchanged":[214],"equations.":[215]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}
