{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T22:49:22Z","timestamp":1777934962270,"version":"3.51.4"},"reference-count":28,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2013,5,1]],"date-time":"2013-05-01T00:00:00Z","timestamp":1367366400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Mechanics of Solids"],"published-print":{"date-parts":[[2014,7]]},"abstract":"<jats:p>In this paper we discuss the consequences of the distributional approach to dislocations in terms of the mathematical properties of the auxiliary model fields such as displacement and displacement gradient which are obtained directly from the main model field here considered as the linear strain. We show that these fields cannot be introduced rigourously without the introduction of gauge fields or, equivalently, without cuts in the Riemann foliation associated with the dislocated crystal. In a second step we show that the space of bounded deformations follows from the distributional approach in a natural way and discuss the reasons why it is adequate to model dislocations. The case of dislocation clusters is also addressed, as it represents an important issue in industrial crystal growth while from a mathematical point of view, peculiar phenomena might appear at the set of accumulation points. The elastic\u2013plastic decomposition of the strain within this approach is also given a precise meaning.<\/jats:p>","DOI":"10.1177\/1081286513479196","type":"journal-article","created":{"date-parts":[[2013,5,2]],"date-time":"2013-05-02T04:05:03Z","timestamp":1367467503000},"page":"579-600","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Fields of bounded deformation for mesoscopic dislocations"],"prefix":"10.1177","volume":"19","author":[{"given":"Nicolas","family":"Van Goethem","sequence":"first","affiliation":[{"name":"Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy; Universidade de Lisboa, Faculdade de Ci\u00eancias, Departamento de Matem\u00e1tica, CMAF, Lisboa, Portugal"}]}],"member":"179","published-online":{"date-parts":[[2013,5,1]]},"reference":[{"key":"bibr1-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792512000010"},{"key":"bibr2-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1007\/s11565-012-0149-5"},{"key":"bibr3-1081286513479196","volume-title":"Th\u00e9orie des distributions","author":"Schwartz L","year":"1957"},{"key":"bibr4-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-007-0120-y"},{"key":"bibr5-1081286513479196","doi-asserted-by":"publisher","DOI":"10.3934\/jgm.2010.2.303"},{"key":"bibr6-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2006.1699"},{"key":"bibr7-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2011.07.023"},{"key":"bibr8-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.201100076"},{"key":"bibr9-1081286513479196","volume-title":"Lectures at the Vienna Summer School on Microstructures","author":"Ortiz M","year":"2000"},{"key":"bibr10-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1007\/BF00284617"},{"key":"bibr11-1081286513479196","volume-title":"Theory of dislocations","author":"Hirth J","year":"1982","edition":"2"},{"key":"bibr12-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1142\/0356"},{"key":"bibr13-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1007\/s10659-010-9275-4"},{"key":"bibr14-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechrescom.2012.08.009"},{"key":"bibr15-1081286513479196","volume-title":"Physiques des d\u00e9fauts, Les Houches session XXXV (Course 3)","author":"Kr\u00f6ner E","year":"1980"},{"key":"bibr16-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1007\/s10701-010-9440-4"},{"key":"bibr17-1081286513479196","series-title":"Oxford Mathematical Monographs","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502456.001.0001","volume-title":"Functions of bounded variation and free discontinuity problems","author":"Ambrosio L","year":"2000"},{"key":"bibr18-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2004.07.006"},{"key":"bibr19-1081286513479196","volume-title":"Analyse harmonique r\u00e9elle","author":"Willem M","year":"1995"},{"key":"bibr20-1081286513479196","doi-asserted-by":"publisher","DOI":"10.5802\/aif.204"},{"key":"bibr21-1081286513479196","doi-asserted-by":"publisher","DOI":"10.1007\/b98245"},{"key":"bibr22-1081286513479196","unstructured":"Ebobisse F. 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