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Infinite-order laminates in a model in crystal plasticity

Albin, Nathan and Conti, Sergio and Dolzmann, Georg (2009) Infinite-order laminates in a model in crystal plasticity. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 139 (4). pp. 685-708. ISSN 0308-2105.

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We consider a geometrically nonlinear model for crystal plasticity in two dimensions, with two active slip systems and rigid elasticity. We prove that the rank-1 convex envelope of the condensed energy density is obtained by infinite-order laminates, and express it explicitly via the _(2)F_1 hypergeometric function. We also determine the polyconvex envelope, leading to upper and lower bounds on the quasiconvex envelope. The two bounds differ by less than 2%.

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Additional Information:© 2009 Royal Society of Edinburgh. MS received 14 January 2008; accepted 29 July 2008. This work was performed while N.A. was at the Universität Duisburg-Essen, supported by the National Science Foundation through the Mathematical Sciences Postdoctoral Research Fellowship Award no. 0603611. The work of S.C. was supported by the Deutsche Forschungsgemeinschaft through Schwerpunktprogramm. 1253, 'Optimization with Partial Differential Equations', Project no. CO 304/2-l. The work of G.D. was supported by the National Science Foundation through Grant no. DMS 0405853.
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NSFDMS 0405853
Deutsche ForschungsgemeinschaftCO 304/2-1
Issue or Number:4
Record Number:CaltechAUTHORS:20090818-151440414
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15161
Deposited By: Jason Perez
Deposited On:19 Aug 2009 17:11
Last Modified:26 Dec 2012 11:13

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