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Bhattacharya, K.; James, R. D.

A theory of thin films of martensitic materials with applications to microactuators. (English) Zbl 0960.74046

J. Mech. Phys. Solids 47, No. 3, 531-576 (1999).
From the summary: We give a direct derivation of a theory for single crystal thin films, starting from three-dimensional nonlinear elasticity 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, untwinned 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.

Cited in 3 Reviews
Cited in 61 Documents

MSC:

74K35 Thin films
74G65 Energy minimization in equilibrium problems in solid mechanics
74A35 Polar materials
74N05 Crystals in solids

Keywords:

higher order theories; bending energy; phase transformation; shape memory effect; microactuator; variational calculus; single crystal thin films; three-dimensional nonlinear elasticity; interfacial energy; asymptotic expansion; frame-indifferent Cosserat membrane theory; Cosserat vector field; multi-well energy functions; martensitic materials
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