{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T01:01:49Z","timestamp":1793062909533,"version":"4.5.0"},"reference-count":51,"publisher":"American Physical Society (APS)","issue":"5","license":[{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-license"},{"start":{"date-parts":[[2026,11,4]],"date-time":"2026-11-04T00:00:00Z","timestamp":1793750400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-accepted-manuscript-license"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DGE-2244310"],"award-info":[{"award-number":["DGE-2244310"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CMMI-1901959"],"award-info":[{"award-number":["CMMI-1901959"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF-23-1-0032"],"award-info":[{"award-number":["W911NF-23-1-0032"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2025,10,9]]},"DOI":"10.1103\/42dk-54hl","type":"journal-article","created":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:20:47Z","timestamp":1760034047000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Particle-scale origin of quadrupolar nonaffine displacement fields in granular solids"],"prefix":"10.1103","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-4128-0378","authenticated-orcid":true,"given":"Evan P.","family":"Willmarth","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03v76x132","id-type":"ROR","asserted-by":"publisher"}],"name":"Yale University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9901-4642","authenticated-orcid":true,"given":"Weiwei","family":"Jin","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03v76x132","id-type":"ROR","asserted-by":"publisher"}],"name":"Yale University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7588-9532","authenticated-orcid":true,"given":"Dong","family":"Wang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03v76x132","id-type":"ROR","asserted-by":"publisher"}],"name":"Yale University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1776-0642","authenticated-orcid":true,"given":"Amit","family":"Datye","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03v76x132","id-type":"ROR","asserted-by":"publisher"}],"name":"Yale University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5361-0342","authenticated-orcid":true,"given":"Udo D.","family":"Schwarz","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03v76x132","id-type":"ROR","asserted-by":"publisher"}],"name":"Yale University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8473-2505","authenticated-orcid":true,"given":"Mark D.","family":"Shattuck","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00wmhkr98","id-type":"ROR","asserted-by":"publisher"}],"name":"City College of The City University of New York"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8272-5640","authenticated-orcid":true,"given":"Corey S.","family":"O'Hern","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03v76x132","id-type":"ROR","asserted-by":"publisher"}],"name":"Yale University"},{"id":[{"id":"https:\/\/ror.org\/03v76x132","id-type":"ROR","asserted-by":"publisher"}],"name":"Yale University"},{"id":[{"id":"https:\/\/ror.org\/03v76x132","id-type":"ROR","asserted-by":"publisher"}],"name":"Yale University"},{"id":[{"id":"https:\/\/ror.org\/03v76x132","id-type":"ROR","asserted-by":"publisher"}],"name":"Yale University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,11,4]]},"reference":[{"key":"42dk-54hlCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.016118","type":"journal-article"},{"key":"42dk-54hlCc2R1","doi-asserted-by":"publisher","DOI":"10.1039\/D1SM00898F","type":"journal-article"},{"key":"42dk-54hlCc3R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apmt.2021.100958","type":"journal-article"},{"key":"42dk-54hlCc4R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.11.041019","type":"journal-article"},{"key":"42dk-54hlCc5R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.95.144201","type":"journal-article"},{"key":"42dk-54hlCc6R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.127.015501","type":"journal-article"},{"key":"42dk-54hlCc7R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevMaterials.7.105604","type":"journal-article"},{"key":"42dk-54hlCc8R1","doi-asserted-by":"publisher","DOI":"10.1002\/adma.202212086","type":"journal-article"},{"key":"42dk-54hlCc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.93.195501","type":"journal-article"},{"key":"42dk-54hlCc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.109.255502","type":"journal-article"},{"key":"42dk-54hlCc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.109.L053002","type":"journal-article"},{"key":"42dk-54hlCc12R1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1957.0133","type":"journal-article"},{"key":"42dk-54hlCc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.119.195503","type":"journal-article"},{"key":"42dk-54hlCc14R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.94.022907","type":"journal-article"},{"key":"42dk-54hlCc15R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2015.02.017","type":"journal-article"},{"key":"42dk-54hlCc16R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139167970","type":"book","volume-title":"Mechanics of Solid Materials","author":"J. Lemaitre","year":"1990"},{"key":"42dk-54hlCc17R1","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5416(79)90174-5","type":"journal-article"},{"key":"42dk-54hlCc18R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.57.7192","type":"journal-article"},{"key":"42dk-54hlCc19R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jallcom.2023.170585","type":"journal-article"},{"key":"42dk-54hlCc20R1","doi-asserted-by":"publisher","DOI":"10.1557\/s43577-021-00171-8","type":"journal-article"},{"key":"42dk-54hlCc21R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.107.108302","type":"journal-article"},{"key":"42dk-54hlCc22R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.95.098301","type":"journal-article"},{"key":"42dk-54hlCc23R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1412095111","type":"journal-article"},{"key":"42dk-54hlCc24R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jallcom.2016.12.366","type":"journal-article"},{"key":"42dk-54hlCc25R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.110.058001","type":"journal-article"},{"key":"42dk-54hlCc26R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2204879119","type":"journal-article"},{"key":"42dk-54hlCc27R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-025-02008-1","type":"journal-article"},{"key":"42dk-54hlCc28R1","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/113\/54001","type":"journal-article"},{"key":"42dk-54hlCc29R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.170201","type":"journal-article"},{"key":"42dk-54hlCc30R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-54857-z","type":"journal-article"},{"key":"42dk-54hlCc31R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.108.L042901","type":"journal-article"},{"key":"42dk-54hlCc33R1","doi-asserted-by":"publisher","DOI":"10.1039\/D0SM01137A","type":"journal-article"},{"key":"42dk-54hlCc34R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijplas.2023.103760","type":"journal-article"},{"key":"42dk-54hlCc35R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.conbuildmat.2024.137193","type":"journal-article"},{"key":"42dk-54hlCc36R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.107.054903","type":"journal-article"},{"key":"42dk-54hlCc37R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cageo.2011.07.008","type":"journal-article"},{"key":"42dk-54hlCc38R1","volume-title":"Micromechanics of Defects in Solids","author":"T. Mura","year":"2013","type":"book"},{"key":"42dk-54hlCc39R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.103.053003","type":"journal-article"},{"key":"42dk-54hlCc40R1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7683(85)90076-9","type":"journal-article"},{"key":"42dk-54hlCc41R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-7550-8","type":"book","volume-title":"The Finite Element Method and Applications in Engineering Using ANSYS\u00ae","author":"E. Madenci","year":"2015"},{"key":"42dk-54hlCc42R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781316336144","type":"book","volume-title":"Nonlinear Solid Mechanics for Finite Element Analysis: Statics","author":"J. Bonet","year":"2016"},{"key":"42dk-54hlCc43R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139020411","type":"book","volume-title":"Matrix Analysis","author":"R.\u00a0A. Horn","year":"2012"},{"key":"42dk-54hlCc44R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-45671-8","type":"journal-article"},{"key":"42dk-54hlCc45R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.102.033008","type":"journal-article"},{"key":"42dk-54hlCc46R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.93.053002","type":"journal-article"},{"key":"42dk-54hlCc47R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1919958117","type":"journal-article"},{"key":"42dk-54hlCc48R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.063002","type":"journal-article"},{"key":"42dk-54hlCc49R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.77.041505","type":"journal-article"},{"key":"42dk-54hlCc50R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1709015114","type":"journal-article"},{"key":"42dk-54hlCc51R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.055501","type":"journal-article"},{"key":"42dk-54hlCc52R1","unstructured":"E.\u00a0P. Willmarth, W. Jin, D. Wang, A. Datye, U.\u00a0D. Schwarz, M.\u00a0D. Shattuck, and C.\u00a0S. O'Hern, Particle-scale origin of quadrupolar non affine displacement fields in granular solids, https:\/\/github.com\/kinglocc\/discreteEshelby.git.","type":"dataset"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/accepted\/10.1103\/42dk-54hl","content-type":"application\/pdf","content-version":"am","intended-application":"unspecified"},{"URL":"https:\/\/link.aps.org\/article\/10.1103\/42dk-54hl","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/42dk-54hl\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T22:22:22Z","timestamp":1790720542000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/42dk-54hl"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,4]]},"references-count":51,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,11]]}},"URL":"https:\/\/doi.org\/10.1103\/42dk-54hl","relation":{},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,4]]},"assertion":[{"value":"2025-06-21","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"\u00a92025 American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"055402"}}