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. doi:10.1007/s002050050049. 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.
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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). | ||||||||||
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Issue or Number: | 2 | ||||||||||
DOI: | 10.1007/s002050050049 | ||||||||||
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: | 10 Nov 2021 04:33 |
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