{"id":"https://openalex.org/W7154703002","doi":"https://doi.org/10.48550/arxiv.2604.14264","title":"Learning ultra-compressible hyperelasticity with splines: Constitutive asymmetries and non-unique representations","display_name":"Learning ultra-compressible hyperelasticity with splines: Constitutive asymmetries and non-unique representations","publication_year":2026,"publication_date":"2026-04-15","ids":{"openalex":"https://openalex.org/W7154703002","doi":"https://doi.org/10.48550/arxiv.2604.14264"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.14264","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.14264","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.14264","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133608105","display_name":"Miguel Angel Moreno-Mateos","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Moreno-Mateos, Miguel Angel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092733979","display_name":"Simon Wiesheier","orcid":"https://orcid.org/0009-0008-9625-3446"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wiesheier, Simon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133833493","display_name":"Paul Steinmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steinmann, Paul","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133843315","display_name":"Ellen Kuhl","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kuhl, Ellen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.3652999997138977,"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":0.3652999997138977,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.3125999867916107,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.07410000264644623,"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/hyperelastic-material","display_name":"Hyperelastic material","score":0.888700008392334},{"id":"https://openalex.org/keywords/ansatz","display_name":"Ansatz","score":0.6930999755859375},{"id":"https://openalex.org/keywords/isochoric-process","display_name":"Isochoric process","score":0.4390999972820282},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.41370001435279846},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4065999984741211},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.3709000051021576},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.3707999885082245},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.3499999940395355},{"id":"https://openalex.org/keywords/deformation","display_name":"Deformation (meteorology)","score":0.34290000796318054}],"concepts":[{"id":"https://openalex.org/C147370603","wikidata":"https://www.wikidata.org/wiki/Q3801506","display_name":"Hyperelastic material","level":3,"score":0.888700008392334},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.6930999755859375},{"id":"https://openalex.org/C91556481","wikidata":"https://www.wikidata.org/wiki/Q208388","display_name":"Isochoric process","level":2,"score":0.4390999972820282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41780000925064087},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.41370001435279846},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4065999984741211},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3582000136375427},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.3402999937534332},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.3384999930858612},{"id":"https://openalex.org/C20192703","wikidata":"https://www.wikidata.org/wiki/Q17106073","display_name":"Strain energy density function","level":3,"score":0.3278999924659729},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32429999113082886},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.3230000138282776},{"id":"https://openalex.org/C163892269","wikidata":"https://www.wikidata.org/wiki/Q15300737","display_name":"Finite strain theory","level":3,"score":0.30059999227523804},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.29319998621940613},{"id":"https://openalex.org/C138622882","wikidata":"https://www.wikidata.org/wiki/Q7269079","display_name":"Quantum nonlocality","level":4,"score":0.29089999198913574},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.2745000123977661},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.273499995470047},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.271699994802475},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25609999895095825},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25270000100135803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.14264","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.14264","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.14264","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.14264","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.8545747995376587,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Highly":[0],"compressible":[1],"solids,":[2],"such":[3,14,31,192],"as":[4,32,75,193],"foams,":[5,85],"exhibit":[6],"complex":[7,165],"responses,":[8],"including":[9],"pronounced":[10],"tension-compression":[11],"asymmetry.":[12],"Capturing":[13],"behaviors":[15],"within":[16],"unified":[17],"hyperelastic":[18,23],"frameworks":[19],"remains":[20],"challenging.":[21],"Invariant-based":[22],"models":[24,146,219],"are":[25,206,229],"commonly":[26],"identified":[27],"from":[28,112],"standard":[29],"tests":[30],"homogeneous":[33,109],"uniaxial":[34],"tension/compression":[35],"and":[36,54,79,115,125,169,189,199,238],"simple":[37],"shear,":[38],"implicitly":[39],"assuming":[40],"a":[41,66,76,151,184,216],"unique":[42],"energy":[43],"representation.":[44,154],"Here":[45],"we":[46,86],"show":[47],"that":[48,183,200],"this":[49,88],"assumption":[50],"is":[51,64,197],"fundamentally":[52],"violated":[53],"that,":[55],"oftentimes,":[56],"the":[57,98,129,162,175,213],"choice":[58],"of":[59,68,101,123],"which":[60],"term":[61,186],"should":[62],"prevail":[63],"just":[65],"matter":[67],"taste.":[69],"Using":[70],"spline-based":[71],"strain-energy":[72],"density":[73],"functions":[74],"data-adaptive":[77],"tool":[78],"stress-strain":[80],"experimental":[81,110],"data":[82,111],"for":[83],"elastomeric":[84],"expose":[87],"non-uniqueness,":[89],"often":[90],"hidden":[91],"in":[92,105,128,174],"low-parameter":[93],"formulations.":[94],"Our":[95],"framework":[96],"captures":[97],"volumetric":[99,166,190],"deformation":[100,167],"ultra-light":[102],"foams":[103],"used":[104],"racing":[106],"shoes":[107],"using":[108],"tension,":[113],"compression,":[114],"shear.":[116],"We":[117,181],"formulate":[118],"an":[119],"overly":[120],"rich":[121],"ansatz":[122],"separable":[124],"non-separable":[126],"energies":[127],"($\\bar{I}_1$,":[130],"$\\bar{I}_2$,":[131],"$J$)":[132],"space":[133],"\u00e0":[134],"la":[135],"Money-Rivlin.":[136],"These":[137],"constructs,":[138],"defined":[139],"by":[140],"multiplicative":[141],"decompositions,":[142],"resemble":[143],"classical":[144],"invariant-based":[145],"while":[147],"generalizing":[148],"them":[149],"to":[150,160,171,178,232,236],"data-driven":[152],"spline":[153],"This":[155],"serves":[156],"two":[157],"purposes:":[158],"(i)":[159],"capture":[161],"response":[163],"under":[164],"modes":[168],"(ii)":[170],"allow":[172],"non-uniqueness":[173],"identification":[176],"problem":[177],"emerge":[179],"naturally.":[180],"find":[182],"coupling":[185,202],"between":[187],"isochoric":[188],"deformation,":[191],"$\u03a8(\\bar{I}_1,J)$":[194],"or":[195],"$\u03a8(\\bar{I}_2,J)$,":[196],"essential":[198],"additional":[201],"terms":[203],"help":[204],"but":[205,234],"not":[207,230],"fully":[208],"necessary;":[209],"rather,":[210],"they":[211],"pronounce":[212],"non-uniqueness.":[214],"As":[215],"consequence,":[217],"different":[218],"may":[220],"be":[221],"indistinguishable":[222],"on":[223],"available":[224],"data.":[225],"Importantly,":[226],"these":[227],"challenges":[228],"specific":[231],"splines":[233],"extend":[235],"traditional":[237],"neural":[239],"network-based":[240],"models.":[241]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-18T00:00:00"}
