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Published October 1997 | public
Journal Article

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

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.

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).

Additional details

Created:
August 19, 2023
Modified:
October 25, 2023