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Elastic Energy Minimization and the Recoverable Strains of Polycrystalline Shape-Memory Materials

Bhattacharya, Kaushik and Kohn, Robert V. (1997) Elastic Energy Minimization and the Recoverable Strains of Polycrystalline Shape-Memory Materials. Archive for Rational Mechanics and Analysis, 139 (2). pp. 99-180. ISSN 0003-9527. https://resolver.caltech.edu/CaltechAUTHORS:20131007-131619635

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Abstract

Shape‐memory behavior is the ability of certain materials to recover, on heating, apparently plastic deformation sustained below a critical temperature. Some materials have good shape‐memory behavior as single crystals but little or none as polycrystals, while others have good shape‐memory behavior even as polycrystals. We propose a method for explaining the difference. Our approach is based on elastic energy minimization. It leads to a special class of nonlinear homogenization problems, involving integrands that are degenerate near the origin. We explore the behavior of these problems through various examples and bounds. The elementary “Taylor bound” and the newer “translation method” are central to our analysis.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s002050050049 DOIArticle
http://link.springer.com/article/10.1007%2Fs002050050049PublisherArticle
ORCID:
AuthorORCID
Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information:© 1997 Springer-Verlag. Accepted October 26, 1995. Some of this research was conducted while K. Bhattacharya held a postdoctoral position at the Courant Institute. This work was partially supported by grants from ARO (K. Bhattacharya & R.V. Kohn), NSF (K. Bhattacharya & R.V. Kohn), ONR (K. Bhattacharya) and the Powell Foundation (K. Bhattacharya).
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)UNSPECIFIED
NSFUNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Powell FoundationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20131007-131619635
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20131007-131619635
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41717
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Oct 2013 20:55
Last Modified:03 Oct 2019 05:51

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