The inverse magnetostrictive effect, magnetoelastic effect or Villari effect, after its discoverer Emilio Villari, is the change of the magnetic susceptibility of a material when subjected to a mechanical stress.

Explanation

The magnetostriction \lambda characterizes the shape change of a ferromagnetic material during magnetization, whereas the inverse magnetostrictive effect characterizes the change of sample magnetization M(for given magnetizing field strength H) when mechanical stresses \sigma are applied to the sample.

Qualitative explanation of magnetoelastic effect

Under a given uni-axial mechanical stress \sigma, the flux density B for a given magnetizing field strength H may increase or decrease. The way in which a material responds to stresses depends on its saturation magnetostriction \lambda_s. For this analysis, compressive stresses \sigma are considered as negative, whereas tensile stresses are positive. According to Le Chatelier's principle: This means, that when the product is positive, the flux density B increases under stress. On the other hand, when the product is negative, the flux density B decreases under stress. This effect was confirmed experimentally.

Quantitative explanation of magnetoelastic effect

In the case of a single stress \sigma acting upon a single magnetic domain, the magnetic strain energy density E_\sigma can be expressed as: where \lambda_s is the magnetostrictive expansion at saturation, and \theta is the angle between the saturation magnetization and the stress's direction. When \lambda_s and \sigma are both positive (like in iron under tension), the energy is minimum for \theta = 0, i.e. when tension is aligned with the saturation magnetization. Consequently, the magnetization is increased by tension.

Magnetoelastic effect in a single crystal

In fact, magnetostriction is more complex and depends on the direction of the crystal axes. In iron, the [100] axes are the directions of easy magnetization, while there is little magnetization along the [111] directions (unless the magnetization becomes close to the saturation magnetization, leading to the change of the domain orientation from [111] to [100]). This magnetic anisotropy pushed authors to define two independent longitudinal magnetostrictions and.

Method of testing the magnetoelastic properties of magnetic materials

Method suitable for effective testing of magnetoelastic effect in magnetic materials should fulfill the following requirements: Following testing methods were developed:

Applications of magnetoelastic effect

Magnetoelastic effect can be used in development of force sensors. This effect was used for sensors: Inverse magnetoelastic effects have to be also considered as a side effect of accidental or intentional application of mechanical stresses to the magnetic core of inductive component, e.g. fluxgates or generator/motor stators when installed with interference fits.