{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:18:59Z","timestamp":1763468339428},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2016,11,3]],"date-time":"2016-11-03T00:00:00Z","timestamp":1478131200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Eur. J. Appl. Math"],"published-print":{"date-parts":[[2017,8]]},"abstract":"<jats:p>The gradient flow structure of the model introduced in Cermelli &amp; Gurtin (1999, The motion of screw dislocations in crystalline materials undergoing antiplane shear: glide, cross-slip, fine cross-slip. <jats:italic>Arch. Rational Mech. Anal.<\/jats:italic><jats:bold>148<\/jats:bold>(1), 3\u201352) for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the \u201cmaximal dissipation criterion\u201d that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in Cermelli &amp; Gurtin is connected to a time-discrete evolution scheme which explicitly confines dislocations to move at each time step along a single glide direction. It is proved that the time-continuous model in Cermelli &amp; Gurtin is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalisation of standard gradient flow theory that allows for dissipations which cannot be described by a metric.<\/jats:p>","DOI":"10.1017\/s0956792516000462","type":"journal-article","created":{"date-parts":[[2016,11,3]],"date-time":"2016-11-03T03:33:04Z","timestamp":1478143984000},"page":"636-655","source":"Crossref","is-referenced-by-count":4,"title":["Dynamics of screw dislocations: A generalised minimising-movements scheme approach"],"prefix":"10.1017","volume":"28","author":[{"given":"GIOVANNI A.","family":"BONASCHI","sequence":"first","affiliation":[]},{"given":"PATRICK","family":"VAN MEURS","sequence":"additional","affiliation":[]},{"given":"MARCO","family":"MORANDOTTI","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,11,3]]},"reference":[{"key":"S0956792516000462_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s002050050155"},{"key":"S0956792516000462_ref4","doi-asserted-by":"publisher","DOI":"10.1137\/140980065"},{"key":"S0956792516000462_ref9","volume-title":"Introduction to Dislocations","author":"Hull","year":"2001"},{"key":"S0956792516000462_ref7","volume-title":"Piecewise-Smooth Dynamical Systems: Theory and Applications","author":"di Bernardo","year":"2008"},{"key":"S0956792516000462_ref3","volume-title":"Gradient Flows in Metric Spaces and in the Space of Probability Measures","author":"Ambrosio","year":"2008"},{"key":"S0956792516000462_ref10","volume-title":"Theory of Dislocations","author":"Hirth","year":"1982"},{"key":"S0956792516000462_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2016.03.020"},{"key":"S0956792516000462_ref5","article-title":"Renormalized energy and Peach-K\u00f6hler forces for screw dislocations with antiplane shear","volume":"24","author":"Blass","year":"2017","journal-title":"J. Convex Anal."},{"key":"S0956792516000462_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-26883-5_3"},{"key":"S0956792516000462_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-014-0757-6"},{"key":"S0956792516000462_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7793-9"}],"container-title":["European Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0956792516000462","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T21:57:17Z","timestamp":1555451837000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0956792516000462\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,3]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,8]]}},"alternative-id":["S0956792516000462"],"URL":"https:\/\/doi.org\/10.1017\/s0956792516000462","relation":{},"ISSN":["0956-7925","1469-4425"],"issn-type":[{"value":"0956-7925","type":"print"},{"value":"1469-4425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,3]]}}}