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Restrictions on microstructure

Published online by Cambridge University Press:  14 November 2011

Kaushik Bhattacharya ,
Nikan B. Firoozye ,
Richard D. James  and
Robert V. Kohn
Kaushik Bhattacharya
Affiliation:
Div. of Engrng, Caltech, Pasadena, CA 91125, U.S.A.
Nikan B. Firoozye
Affiliation:
Dept. of Mathematics, Univ. of Illinois, Urbana, IL 61801, U.S.A.
Richard D. James
Affiliation:
Aero. Engrng and Mechanics, University of Minnesota, Minneapolis, MN 55455, U.S.A.
Robert V. Kohn
Affiliation:
Courant Institute, 251 Mercer Street, New York, NY 10012, U.S.A.
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Extract

We consider the following question: given a set of matrices with no rank-one connections, does it support a nontrivial Young measure limit of gradients? Our main results are these: (a) a Young measure can be supported on four incompatible matrices; (b) in two space dimensions, a Young measure cannot be supported on finitely many incompatible elastic wells; (c) in three or more space dimensions, a Young measure can be supported on three incompatible elastic wells; and (d) if supports a nontrivial Young measure with mean value 0, then the linear span of must contain a matrix of rank one.

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Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 5 , 1994 , pp. 843 - 878
Copyright
Copyright © Royal Society of Edinburgh 1994

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