  Magnetostrictive wires of diameter in the nanometer scale have been proposed
for application as acoustic sensors [Downey et al., 2008], [Yang et al., 2006].
The sensing mechanism is expected to operate in the bending regime. In this
work we derive a variational theory for the bending of magnetostrictive
nanowires starting from a full 3-dimensional continuum theory of
magnetostriction. We recover a theory which looks like a typical
Euler-Bernoulli bending model but includes an extra term contributed by the
magnetic part of the energy. The solution of this variational theory for an
important, newly developed magnetostricitve alloy called Galfenol (cf. [Clark
et al., 2000]) is compared with the result of experiments on actual nanowires
(cf. [Downey, 2008]) which shows agreement.
