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Published March 1999 | public
Journal Article

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


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.

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).

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