MR E ffect

MR e ffect is one of the key parameters for characterizing the performance of MREs. The change in the behaviors of the MR composite under the magnetic field is expressed by the absolute MR e ffect and the relative MR e ffect [122–125]. The absolute MR e ffect represents the di fference between the shear modulus of the maximum value obtained under the magnetic field and the shear modulus (zero field modulus) when there is no magnetic field as given in Equation (2),

$$
\Delta G = \mathcal{G}\_{\text{max}} - \mathcal{G}\_0 \tag{2}
$$

On the other hand, the relative MR e ffect is the percentage of absolute MR e ffect and zero field modulus *G*0 as follows;

$$
\Delta G\_{\text{V}} = \frac{\Delta G}{G\_0} \times 100\% \tag{3}
$$

As well-known in many studies, the absolute and relative MR e ffects vary with several factors, including oscillation frequency, magnetic field strength, magnetic particle content, particle size, magnetic material, and the MRE matrix. Khairi et al. [97] studied the e ffects of silicone oil plasticizer on MREs. Figure 8 shows the relative MR e ffects of isotropic and anisotropic MREs depending on the amount of silicone oil. Both isotropic and anisotropic MREs show increased relative MR e ffects as silicone oil content increases. The reason is that the maximum value of shear modulus is similar even though the contents of silicone oil are increased, but as the content of silicone oil is increased, the zero-field modulus (G0) of MRE is lowered, which causes a sharp increase in relative MR e ffect. As such, the MR e ffect is considered to be a key parameter in evaluating the performance of the MRE.

**Figure 8.** Relative MR e ffect for (**a**) isotropic MRE and (**b**) anisotropic MRE as a function of magnetic field for di fferent SO contents [97].
