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A theory of thin films of martensitic materials with applications to microactuators

Bhattacharya, K. and James, R. D. (1999) A theory of thin films of martensitic materials with applications to microactuators. Journal of the Mechanics and Physics of Solids, 47 (3). pp. 531-576. ISSN 0022-5096. https://resolver.caltech.edu/CaltechAUTHORS:20131008-080907937

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Abstract

A direct derivation is given of a theory for single crystal thin films, starting from three dimensional nonlinear elasticity theory augmented by a term for interfacial energy. The derivation involves no a priori choice of asymptotic expansion or ansatz. It yields a frame-indifferent Cosserat membrane theory with one Cosserat vector field. The theory is applied to multi-well energy functions appropriate to martensitic materials. It is found that, unlike in bulk materials, which generally only support finely twinned austenite/martensite interfaces as energy minimizing states, the thin film theory predicts the existence of exact, untwined austenite/martensite interfaces. These are used to construct some simple energy minimizing deformations—”tents” and “tunnels”—that could possibly be the basis of simple large-deformation microactuators. Explicit results are given for martensitic materials in the systems NiMnGa, NiTi,NiTiCu, and NiAl. A certain alloy of precise composition Ni_(30.5) Ti_(49.5) Cu_(20.0) is predicted to support a four-sided “tent” on an (001) film, which furthermore is predicted to collapse to the substrate upon heating. A formal derivation is given of higher order theories, which yields two additional Cosserat vectors and an explicit form of the bending energy. The derivation indicates an approach to plate-shell-thin film theories that is rather different from the ones usually followed.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/S0022-5096(98)00043-X DOIArticle
http://www.sciencedirect.com/science/article/pii/S002250969800043XPublisherArticle
ORCID:
AuthorORCID
Bhattacharya, K.0000-0003-2908-5469
James, R. D.0000-0001-6019-6613
Additional Information:© 1999 Elsevier Science Ltd. Received 1 October 1997; in revised form 7 February 1998. We are grateful to Irene Fonseca for her useful suggestions concerning the treatment of boundary conditions in Section 8. This work was supported by AFOSR (K.B.: F49620-95-1-0109 and R.D.J.: F49620-97-1-0187), ONR/DARPA (R.D.J.: N/N00014-92-J-4034 and N00014-95-1-1145) and NSF (K.B.: CMS-9457573 and R.D.J.: DMS-9505077).
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-95-1-0109
Air Force Office of Scientific Research (AFOSR)F49620-97-1-0187
Office of Naval Research (ONR)N00014-92-J-4034
Office of Naval Research (ONR)N00014-95-1-1145
NSFCMS-9457573
NSFDMS-9505077
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Subject Keywords:phase transformation; shape memory effect; thin films; microactuator; variational calculus
Issue or Number:3
Record Number:CaltechAUTHORS:20131008-080907937
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20131008-080907937
Official Citation:K. Bhattacharya, R.D. James, A theory of thin films of martensitic materials withapplications to microactuators, Journal of the Mechanics and Physics of Solids, Volume 47, Issue 3, 1 March 1999, Pages 531-576, ISSN 0022-5096, http://dx.doi.org/10.1016/S0022-5096(98)00043-X. (http://www.sciencedirect.com/science/article/pii/S002250969800043X)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41727
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Oct 2013 22:47
Last Modified:09 Mar 2020 13:18

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