{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T06:05:13Z","timestamp":1775282713344,"version":"3.50.1"},"reference-count":7,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T00:00:00Z","timestamp":1621209600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T00:00:00Z","timestamp":1621209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["1269\/19"],"award-info":[{"award-number":["1269\/19"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004769","name":"Universit\u00e0 degli Studi di Pavia","doi-asserted-by":"publisher","award":["2017 BSR"],"award-info":[{"award-number":["2017 BSR"]}],"id":[{"id":"10.13039\/501100004769","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We rigorously derive linear elasticity as a low energy limit of pure traction nonlinear elasticity. Unlike previous results, we do not impose any restrictive assumptions on the forces, and obtain a full <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Gamma $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u0393<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-convergence result. The analysis relies on identifying the correct reference configuration to linearize about, and studying its relation to the rotations preferred by the forces (<jats:italic>optimal rotations<\/jats:italic>). The <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Gamma $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u0393<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-limit is the standard linear elasticity model, plus a term that penalizes for fluctuations of the reference configurations from the optimal rotations. However, on minimizers this additional term is zero and the limit energy reduces to standard linear elasticity.<\/jats:p>","DOI":"10.1007\/s00332-021-09716-2","type":"journal-article","created":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T11:02:55Z","timestamp":1621249375000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Reference Configurations Versus\u00a0Optimal Rotations: A Derivation of Linear Elasticity from Finite Elasticity for all Traction Forces"],"prefix":"10.1007","volume":"31","author":[{"given":"Cy","family":"Maor","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7456-0065","authenticated-orcid":false,"given":"Maria Giovanna","family":"Mora","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,5,17]]},"reference":[{"key":"9716_CR1","unstructured":"Bryant, R.: Principal curvatures of $${\\mathbb{R}}^{n^2}$$-embedded $$\\text{SO}{(n)}$$ (2018). https:\/\/mathoverflow.net\/q\/313403"},{"key":"9716_CR2","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1023\/A:1016577431636","volume":"10","author":"G Dal Maso","year":"2002","unstructured":"Dal Maso, G., Negri, M., Percivale, D.: Linearized elasticity as $$\\Gamma $$-limit of finite elasticity. Set Valued Anal. 10, 165\u2013183 (2002)","journal-title":"Set Valued Anal."},{"key":"9716_CR3","doi-asserted-by":"publisher","first-page":"1461","DOI":"10.1002\/cpa.10048","volume":"55","author":"G Friesecke","year":"2002","unstructured":"Friesecke, G., James, R.D., M\u00fcller, S.: A theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity. Commun. Pure Appl. Math. 55, 1461\u20131506 (2002)","journal-title":"Commun. Pure Appl. Math."},{"key":"9716_CR4","doi-asserted-by":"crossref","unstructured":"Jesenko, M., Schmidt, B.: Geometric linearization of theories for incompressible elastic materials and applications (2020). arXiv:2004.11271","DOI":"10.1142\/S0218202521500202"},{"key":"9716_CR5","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/s00033-020-01377-7","volume":"71","author":"E Mainini","year":"2020","unstructured":"Mainini, E., Percivale, D.: Variational linearization of pure traction problems in incompressible elasticity. Z. Angew. Math. Phys. 71, 146 (2020)","journal-title":"Z. Angew. Math. Phys."},{"key":"9716_CR6","doi-asserted-by":"publisher","first-page":"1091","DOI":"10.1007\/s00205-019-01408-2","volume":"234","author":"F Maddalena","year":"2019","unstructured":"Maddalena, F., Percivale, D., Tomarelli, F.: The gap in pure traction problems between linear elasticity and variational limit of finite elasticity. Arch. Ration. Mech. Anal. 234, 1091\u20131120 (2019)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"9716_CR7","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/s10957-019-01533-8","volume":"182","author":"F Maddalena","year":"2019","unstructured":"Maddalena, F., Percivale, D., Tomarelli, F.: A new variational approach to linearization of traction problems in elasticity. J. Optim. Theory Appl. 182, 383\u2013403 (2019)","journal-title":"J. Optim. Theory Appl."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-021-09716-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-021-09716-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-021-09716-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,25]],"date-time":"2021-05-25T16:10:23Z","timestamp":1621959023000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-021-09716-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,17]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["9716"],"URL":"https:\/\/doi.org\/10.1007\/s00332-021-09716-2","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,17]]},"assertion":[{"value":"15 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 May 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"62"}}