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.
characterizes the shape change of a ferromagnetic material during magnetization, whereas the inverse magnetostrictive effect characterizes the change of sample magnetization
(for given magnetizing field strength
[1] Under a given uni-axial mechanical stress
for a given magnetizing field strength
The way in which a material responds to stresses depends on its saturation magnetostriction
For this analysis, compressive stresses
are considered as negative, whereas tensile stresses are positive.
According to Le Chatelier's principle:
This effect was confirmed experimentally.
[2] In the case of a single stress
acting upon a single magnetic domain, the magnetic strain energy density
is the magnetostrictive expansion at saturation, and
is the angle between the saturation magnetization and the stress's direction.
are both positive (like in iron under tension), the energy is minimum for
= 0, i.e. when tension is aligned with the saturation magnetization.
Consequently, the magnetization is increased by tension.
In fact, magnetostriction is more complex and depends on the direction of the crystal axes.
This magnetic anisotropy pushed authors to define two independent longitudinal magnetostrictions
Method suitable for effective testing of magnetoelastic effect in magnetic materials should fulfill the following requirements:[3] Following testing methods were developed: Magnetoelastic effect can be used in development of force sensors.
[8][9] 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.