In the linear region of actuation and sensing (assuming the vector quantities along the direction of maximum response) the constitutive equations of magnetostriction are given by

where S is the strain, σ the mechanical stress, H the magnetic field intensity and B the flux density. The compliance value at a constant magnetic intensity is denoted by s^H,d is the magneto–mechanical constant and µ^σ is the permeability of the medium under constant stress condition. The equations are of the same form as that of piezoelectricity. However, the study of any typical S–H and B–H curve [10-20] brings out the following observations.

The relationship between magnetostriction and applied magnetic field is highly dependent on the intensity of the magnetic field. The relationship is approximately linear when the intensity of the applied magnetic field H is much lower than the intensity of the polarizing field H_pol (field at which the magnetic domains are initially aligned). The non-linearity begins as H approaches H_pol and the curve gradually flattens out signifying saturation or completion of all the domain alignments. Typically, for Terfenol-D rods under stress-free condition, such a relationship is approximately linear in the range of magnetic field from 0 to 100 Orsted.

The maximum free strain generated by magnetostriction is quite large, almost twice as much as that of PZT. Yet, unlike piezoelectric material, the reversal of magnetic field does not result in the reversal of strain here. Particularly, for dynamic applications like vibration suppressions, reversal of actuation strain is very much necessary. Hence, for such applications these actuators are operated with a biased magnetic field such that with respect to the biasing centre, reversal of strain occurs. The technique, however, reduces the availability of actuation strain by approximately 50%; thus lowering its edge over the piezoelectric materials.

It is observed that hysteresis is present in the B–H curve and is usually absent in the B–S curve. As a result, the combination of the two curves shows hysteresis in the S-H curve. The extent of hysteresis depends on the stoichiometry of the material and pre-stressing on the actuator.