Mathematical modeling of magnetostrictive nanowires for sensors/devices with application to Galfenol

Magnetostrictive wires of diameter in the nanometer scale have been proposed for ap-plication as acoustic sensors [Downey et al., 2008], [Yang et al., 2006]. The sensing mech-anism 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 devel-oped magnetostricitve alloy called Galfenol cf. [Clark et al., 2000] is compared with the result of experiments on actual nanowire