Published August 2009
| Published
Journal Article
Open
Infinite-order laminates in a model in crystal plasticity
- Creators
- Albin, Nathan
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Conti, Sergio
- Dolzmann, Georg
Abstract
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%.
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.Attached Files
Published - Albin2009p5571P_Roy_Soc_Edinb_A.pdf
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Additional details
- Eprint ID
- 15161
- Resolver ID
- CaltechAUTHORS:20090818-151440414
- 0603611
- NSF
- DMS 0405853
- NSF
- CO 304/2-1
- Deutsche Forschungsgemeinschaft
- Created
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2009-08-19Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field