Mathematical modeling of magnetostrictive nanowires for sensor application

TL;DR

This paper develops a variational bending model for magnetostrictive nanowires, incorporating magnetic energy effects, and validates it against experimental data for Galfenol nanowires used in sensor applications.

Contribution

It introduces a novel variational theory for magnetostrictive nanowire bending that integrates magnetic energy, extending classical Euler-Bernoulli models.

Findings

The model aligns well with experimental results for Galfenol nanowires.

Magnetic energy significantly influences nanowire bending behavior.

The theory provides a foundation for designing magnetostrictive nanowire sensors.

Abstract

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.