{"id":"https://openalex.org/W7221572989","doi":"https://doi.org/10.48550/arxiv.2610.13874","title":"Potential energy release rate for solids with bounded domains during evolutions involving changes to boundaries and boundary data","display_name":"Potential energy release rate for solids with bounded domains during evolutions involving changes to boundaries and boundary data","publication_year":2026,"publication_date":"2026-10-09","ids":{"openalex":"https://openalex.org/W7221572989","doi":"https://doi.org/10.48550/arxiv.2610.13874"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.13874","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13874","pdf_url":"https://arxiv.org/pdf/2610.13874","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/2610.13874","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039639481","display_name":"Mrityunjay Kothari","orcid":"https://orcid.org/0000-0002-9831-3931","observed_orcids":["https://orcid.org/0000-0002-9831-3931"]},"institutions":[{"id":"https://openalex.org/I161057412","display_name":"University of New Hampshire","ror":"https://ror.org/01rmh9n78","country_code":"US","type":"education","lineage":["https://openalex.org/I161057412"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kothari, Mrityunjay","raw_affiliation_strings":["Department of Mechanical Engineering and Integrated Applied Mathematics , University of New Hampshire , Durham , New Hampshire 03824 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and Integrated Applied Mathematics , University of New Hampshire , Durham , New Hampshire 03824 , USA","institution_ids":["https://openalex.org/I161057412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068483306","display_name":"Sayaka Kochiyama","orcid":"https://orcid.org/0000-0002-5709-1527","observed_orcids":["https://orcid.org/0000-0002-5709-1527"]},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kochiyama, Sayaka","raw_affiliation_strings":["School of Engineering , Brown University , Providence , Rhode Island 02912 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering , Brown University , Providence , Rhode Island 02912 , USA","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078594023","display_name":"Haneesh Kesari","orcid":"https://orcid.org/0000-0001-9761-5754","observed_orcids":["https://orcid.org/0000-0001-9761-5754"]},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kesari, Haneesh","raw_affiliation_strings":["School of Engineering , Brown University , Providence , Rhode Island 02912 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering , Brown University , Providence , Rhode Island 02912 , USA","institution_ids":["https://openalex.org/I27804330"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T13261","display_name":"Elasticity and Wave Propagation","score":0.26100000739097595,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T13261","display_name":"Elasticity and Wave Propagation","score":0.26100000739097595,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.24539999663829803,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10396","display_name":"Fatigue and fracture mechanics","score":0.13439999520778656,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/nonlinear-elasticity","display_name":"nonlinear elasticity","score":0.8700000047683716},{"id":"https://openalex.org/keywords/bounded-domains","display_name":"bounded domains","score":0.640999972820282},{"id":"https://openalex.org/keywords/material-evolution","display_name":"material evolution","score":0.5519999861717224},{"id":"https://openalex.org/keywords/j-integral","display_name":"J-integral","score":0.6700000166893005},{"id":"https://openalex.org/keywords/variational-problems","display_name":"variational problems","score":0.6349999904632568},{"id":"https://openalex.org/keywords/closed-form-expressions","display_name":"closed-form expressions","score":0.5120000243186951}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6754999756813049},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5909000039100647},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5338000059127808},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5159000158309937},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48190000653266907},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.48159998655319214},{"id":"https://openalex.org/C84551667","wikidata":"https://www.wikidata.org/wiki/Q155640","display_name":"Potential energy","level":2,"score":0.4788999855518341},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.43380001187324524},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4235999882221222},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40070000290870667},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39989998936653137},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.382099986076355},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3427000045776367},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C134121241","wikidata":"https://www.wikidata.org/wiki/Q899301","display_name":"Yield (engineering)","level":2,"score":0.32330000400543213},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.29179999232292175},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2754000127315521},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2736000120639801},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C135136745","wikidata":"https://www.wikidata.org/wiki/Q908074","display_name":"Dynamic equilibrium","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.2578999996185303}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.13874","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13874","pdf_url":"https://arxiv.org/pdf/2610.13874","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.2610.13874","doi":"https://doi.org/10.48550/arxiv.2610.13874","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.13874","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.13874","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13874","pdf_url":"https://arxiv.org/pdf/2610.13874","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221572989.pdf","grobid_xml":"https://content.openalex.org/works/W7221572989.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2124767737","https://openalex.org/W2034403443","https://openalex.org/W1997583903","https://openalex.org/W7117113112","https://openalex.org/W2047945541","https://openalex.org/W7009945272","https://openalex.org/W2618756107","https://openalex.org/W1973272844","https://openalex.org/W2095125166","https://openalex.org/W291029281"],"abstract_inverted_index":{"We":[0,30],"investigate":[1],"the":[2,51,63,66,79,91,108,140,144,150,153,167,170,183,190],"rate":[3,54,111,187],"of":[4,6,39,46,65,172],"change":[5,93],"equilibrium":[7,81,85,141,158],"potential":[8,67,95],"energy":[9,68,96],"for":[10,49,107,112,118],"nonlinear":[11],"elastic":[12,178],"solids":[13,113],"undergoing":[14],"evolutions":[15],"that":[16,182],"may":[17],"involve":[18],"changes":[19],"in":[20,94,175],"body":[21,179],"geometry,":[22],"material":[23,121,124],"properties,":[24],"applied":[25],"tractions,":[26],"and":[27,42,126,130,148,180],"prescribed":[28,131],"displacements.":[29],"represent":[31,90],"such":[32],"an":[33],"evolution":[34,71],"by":[35,139,149],"a":[36,44,104,173,176],"one-parameter":[37],"family":[38],"variational":[40,75],"problems":[41,159],"identify":[43],"class":[45],"these":[47],"families":[48],"which":[50],"potential-energy":[52,109,185],"release":[53,110,186],"is":[55,60,136],"well":[56],"defined.":[57],"Particular":[58],"attention":[59],"given":[61],"to":[62,169,189],"formulation":[64],"at":[69,143],"each":[70,73],"state:":[72],"constituent":[74],"problem":[76],"must":[77,87],"yield":[78],"appropriate":[80],"state,":[82],"while":[83],"its":[84],"value":[86],"also":[88],"correctly":[89],"physical":[92],"between":[97],"states.":[98],"Within":[99],"this":[100],"framework,":[101],"we":[102,165],"derive":[103],"closed-form":[105],"expression":[106,135],"with":[114],"bounded":[115],"domains,":[116],"allowing":[117],"spatially":[119],"nonuniform":[120],"evolution,":[122,155],"sharp":[123],"interfaces,":[125],"evolving":[127],"boundary":[128,132],"geometry":[129],"data.":[133],"The":[134],"determined":[137],"entirely":[138],"solution":[142],"state":[145],"under":[146],"consideration":[147],"quantities":[151],"prescribing":[152],"local":[154],"so":[156],"neighboring":[157],"need":[160],"not":[161],"be":[162],"solved.":[163],"Finally,":[164],"apply":[166],"result":[168],"extension":[171],"notch":[174],"two-dimensional":[177],"show":[181],"resulting":[184],"reduces":[188],"classical":[191],"$J$-integral.":[192]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-13T00:00:00"}