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

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.