{"id":"https://openalex.org/W7129021800","doi":"https://doi.org/10.48550/arxiv.2602.12694","title":"Discovering the mechanics of ultra-low density elastomeric foams in elite-level racing shoes","display_name":"Discovering the mechanics of ultra-low density elastomeric foams in elite-level racing shoes","publication_year":2026,"publication_date":"2026-02-13","ids":{"openalex":"https://openalex.org/W7129021800","doi":"https://doi.org/10.48550/arxiv.2602.12694"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.12694","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.12694","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.12694","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055646711","display_name":"Jeremy A. McCulloch","orcid":"https://orcid.org/0009-0003-1960-2124"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"McCulloch, Jeremy A.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126125360","display_name":"Scott L. Delp","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Delp, Scott L.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5005701510","display_name":"Ellen Kuhl","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kuhl, Ellen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055646711"],"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/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.18569999933242798,"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/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.18569999933242798,"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/T11018","display_name":"Lower Extremity Biomechanics and Pathologies","score":0.15330000221729279,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.08470000326633453,"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/elastomer","display_name":"Elastomer","score":0.7752000093460083},{"id":"https://openalex.org/keywords/stiffness","display_name":"Stiffness","score":0.6121000051498413},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.45089998841285706},{"id":"https://openalex.org/keywords/constitutive-equation","display_name":"Constitutive equation","score":0.412200003862381},{"id":"https://openalex.org/keywords/hysteresis","display_name":"Hysteresis","score":0.40709999203681946},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.39660000801086426},{"id":"https://openalex.org/keywords/shear","display_name":"Shear (geology)","score":0.37709999084472656},{"id":"https://openalex.org/keywords/energy-density","display_name":"Energy density","score":0.36309999227523804}],"concepts":[{"id":"https://openalex.org/C38052585","wikidata":"https://www.wikidata.org/wiki/Q252266","display_name":"Elastomer","level":2,"score":0.7752000093460083},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.6251999735832214},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.6121000051498413},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.45089998841285706},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.42089998722076416},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.412200003862381},{"id":"https://openalex.org/C123299182","wikidata":"https://www.wikidata.org/wiki/Q190837","display_name":"Hysteresis","level":2,"score":0.40709999203681946},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.39660000801086426},{"id":"https://openalex.org/C96035792","wikidata":"https://www.wikidata.org/wiki/Q43606218","display_name":"Shear (geology)","level":2,"score":0.37709999084472656},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.3732999861240387},{"id":"https://openalex.org/C2983502797","wikidata":"https://www.wikidata.org/wiki/Q828402","display_name":"Energy density","level":2,"score":0.36309999227523804},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3564000129699707},{"id":"https://openalex.org/C18140158","wikidata":"https://www.wikidata.org/wiki/Q7079901","display_name":"Ogden","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.35339999198913574},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C107240024","wikidata":"https://www.wikidata.org/wiki/Q184550","display_name":"Mechanical energy","level":3,"score":0.32269999384880066},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C30407753","wikidata":"https://www.wikidata.org/wiki/Q186191","display_name":"Compressive strength","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2669999897480011},{"id":"https://openalex.org/C41279357","wikidata":"https://www.wikidata.org/wiki/Q461466","display_name":"Shear modulus","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.12694","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.12694","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.12694","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.12694","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"score":0.9088845252990723,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Ultra-low-density":[0],"elastomeric":[1,58,226],"foams":[2,19,60,77,104,172,227],"enable":[3,186],"lightweight":[4],"systems":[5],"that":[6,165],"combine":[7],"high":[8,25],"compliance":[9],"with":[10,86,149,173,228],"efficient":[11,28,100],"energy":[12,29,101,135],"return.":[13,102],"In":[14],"high-performance":[15,192],"racing":[16,64,193],"shoes,":[17],"these":[18,142,184],"are":[20],"critical":[21],"for":[22,219],"low":[23,95],"weight,":[24],"cushioning,":[26],"and":[27,39,47,70,73,94,188,201,216,235],"return;":[30],"yet,":[31],"their":[32],"constitutive":[33,145,220],"behavior":[34],"remains":[35],"difficult":[36],"to":[37,50,92,177,195,230],"model":[38],"poorly":[40],"understood.":[41],"Here":[42],"we":[43,152],"integrate":[44],"mechanical":[45],"testing":[46],"machine":[48],"learning":[49],"discover":[51,153],"the":[52,119,167,171],"mechanics":[53],"of":[54,98,170,191,222],"two":[55],"ultra-low":[56],"density":[57],"polymeric":[59],"used":[61],"in":[62],"elite-level":[63],"shoes.":[65],"Across":[66],"uniaxial":[67],"tension,":[68],"confined":[69],"unconfined":[71],"compression,":[72],"simple":[74],"shear,":[75],"both":[76],"exhibit":[78],"pronounced":[79],"tension-compression":[80],"asymmetry,":[81],"negligible":[82],"lateral":[83,129],"strains":[84],"consistent":[85],"an":[87,99,205],"effective":[88],"Poisson's":[89],"ratio":[90],"close":[91,176],"zero,":[93],"hysteresis":[96],"indicative":[97],"Both":[103],"provide":[105],"a":[106,126,132,180,214],"similar":[107],"compressive":[108],"stiffness":[109,121],"(268kPa":[110],"vs.":[111,123,138],"299kPa),":[112],"while":[113],"one":[114],"foam":[115],"exhibits":[116],"nearly":[117],"double":[118],"shear":[120],"(219kPa":[122],"117kPa),":[124],"implying":[125],"substantially":[127],"greater":[128],"stability":[130],"at":[131],"comparable":[133],"vertical":[134],"return":[136],"(83%":[137],"89%).":[139],"By":[140],"integrating":[141],"data":[143],"into":[144],"neural":[146],"networks,":[147],"paired":[148],"sparse":[150],"regression,":[151],"compact,":[154],"interpretable":[155,217],"single-invariant":[156],"models,":[157],"supplemented":[158],"by":[159],"mixed-invariant":[160],"or":[161],"principal-stretch":[162],"based":[163],"terms,":[164],"capture":[166],"unique":[168],"signature":[169],"R2":[174],"values":[175],"one.":[178],"From":[179],"human":[181],"performance":[182,199],"perspective,":[183],"models":[185],"finite-element":[187],"gait-level":[189],"simulations":[190],"shoes":[194],"quantify":[196],"running":[197],"economy,":[198],"enhancements,":[200],"injury":[202],"risks":[203],"on":[204],"individual":[206],"athlete":[207],"level.":[208],"More":[209],"broadly,":[210],"this":[211],"work":[212],"establishes":[213],"scalable":[215],"approach":[218],"modeling":[221],"highly":[223],"compressible,":[224],"ultra-light":[225],"applications":[229],"wearable":[231],"technologies,":[232],"soft":[233],"robotics,":[234],"energy-efficient":[236],"mobility":[237],"systems.":[238]},"counts_by_year":[],"updated_date":"2026-02-17T06:10:05.244387","created_date":"2026-02-17T00:00:00"}