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Infinite-order laminates in a model in crystal plasticity

Published online by Cambridge University Press:  08 July 2009

Nathan Albin ,
Sergio Conti  and
Georg Dolzmann
Nathan Albin
Affiliation:
Applied and Computational Mathematics, California Institute of Technology, 1200 E. California Boulevard, MC 217-50, Pasadena, CA 91101, USA
Sergio Conti
Affiliation:
Fachbereich Mathematik, Universität Duisburg-Essen, 47057 Duisburg, Germany
Georg Dolzmann
Affiliation:
NWF-I Mathematik, Universität Regensburg, 93040 Regensburg, Germany
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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 2F1 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%.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 4 , August 2009 , pp. 685 - 708
Copyright
Copyright © Royal Society of Edinburgh 2009

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