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Restrictions on microstructure

Bhattacharya, Kaushik and Firoozye, Nikan B. and James, Richard D. and Kohn, Robert V. (1994) Restrictions on microstructure. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 124 (5). pp. 843-878. ISSN 0308-2105. https://resolver.caltech.edu/CaltechAUTHORS:20160127-093548090

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1017/S0308210500022381DOIArticle
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8246501&fulltextType=RA&fileId=S0308210500022381PublisherArticle
ORCID:
AuthorORCID
Bhattacharya, Kaushik0000-0003-2908-5469
James, Richard D.0000-0001-6019-6613
Additional Information:© 1994 Royal Society of Edinburgh. Received February 10 1993. Accepted June 12 1993.
Issue or Number:5
Record Number:CaltechAUTHORS:20160127-093548090
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160127-093548090
Official Citation:Kaushik Bhattacharya, Nikan B. Firoozye, Richard D. James and Robert V. Kohn (1994). Restrictions on microstructure. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 124, pp 843-878. doi:10.1017/S0308210500022381.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64003
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:27 Jan 2016 18:36
Last Modified:09 Mar 2020 13:18

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