Inverse magnetostrictive effect
The inverse magnetostrictive effect, magnetoelastic effect or Villari effect is the change of the magnetic susceptibility of a material when subjected to a mechanical stress. Explanation. The magnetostriction formula_1 characterizes the shape change of a ferromagnetic material during magnetization, whereas the inverse magnetostrictive effect characterizes the change of sample magnetization formula_2(for given magnetizing field strength formula_3) when mechanical stresses formula_4 are applied to the sample. Qualitative explanation of magnetoelastic effect. Under a given uni-axial mechanical stress formula_4, the flux density formula_6 for a given magnetizing field strength formula_3 may increase or decrease. The way in which  a material responds to stresses depends on its saturation magnetostriction formula_8. For this analysis, compressive stresses formula_4 are considered as negative, whereas tensile stresses are positive. According to Le Chatelier's principle: formula_10 This means, that when the product formula_11 is positive, the flux density formula_6 increases under stress. On the other hand, when the product formula_11 is negative, the flux density formula_6 decreases under stress. This effect was confirmed experimentally. Quantitative explanation of magnetoelastic effect. In the case of a single stress formula_4 acting upon a single magnetic domain, the magnetic strain energy density formula_16 can be expressed as : formula_17 where formula_8 is the magnetostrictive expansion at saturation, and formula_19 is the angle between the saturation magnetization and the stress's direction. When formula_8 and formula_4 are both positive (like in iron under tension), the energy is minimum for formula_19 = 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  axes are the directions of easy magnetization, while there is little magnetization along the  directions  (unless the magnetization becomes close to the saturation magnetization, leading to the change of the domain orientation from  to ). This magnetic anisotropy pushed authors to define two independent longitudinal magnetostrictions formula_23 and formula_24. 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.