# Magneto-Rheological Elastomer Composites. A Review
## 1 Introduction
This effect, the so-called magnetostriction effect, is due to the decrease of the deformation (\(\epsilon\)) as a function of the inverse square root of the elasticity modulus (\(E\)), (\(\epsilon\)\(\sim\)\(E^{-1/2}\)). Classic elastomer composites, with reinforcing fillers, are prepared by exploiting the long chains cross-linking during the curing process. Generally, the above reported effect is very low for stiff elastomer composites, but the application of an external magnetic field can contribute to a considerable increase of the MRE's elastic modulus, up to 30%. As reported in literature by [PERSON] at al., this affects the resonance frequency and the damping behavior of the adaptive components [15]. The mechanism of materials magnetization is described in Figure 2.  
Figure 1: Magneto–rheological (MR) fluid to magneto-rheological elastomer (MRE) transition as a function of temperature. Reprinted from [3], © 2005 with permission from RSC. The metal particles used as fillers for the MRE composites greatly affect their properties; thus, saturation magnetization and magnetic coercivity result key parameters for the adoptive components. Considering the easy reversibility of the magnetization direction, the energy dissipation in an alternating magnetic field is very low. At the same time, when an external magnetic field is applied, the particles magnetization and the magnetic flux density of the composite increase, and as a result interaction between neighboring particles increases. The MRE's triggering occurs at the application of the external magnetic field because the magnetization of the fillers lead to a rapid and stepwise change in magnetic flux. Among the adjacent magnetic particles dipole-dipole interactions are generated which stiffens the matrix; thus, forcing the fillers to arrange themselves in a columnar structure. This particular particle distribution is easily reached when a magnetic field is applied during the curing process. This distribution effect determines the MREs composite's switching ability and,  
Figure 2: Schematic representation the describing the mechanism for the magnetization: (**a**) demagnetized stage, (**b**) low strain region—domain wall motion stage, (**c**) rotation (closest to the applied field) stage, and (**d**) saturation (alignment with applied field) stage. since stiffness and hysteresis behaviors depend on the magnetic orientation, an anisotropic composite can be easily prepared by exploiting this behavior. The energy interaction of the magnetic particles (\(E_{MI}\)) increases as a function of the magnetic dipole moment square, and decreases with the third power of the average distance among the adjacent fillers \(E_{MI}=V_{p}^{2}/\langle r\rangle^{3}\). The particle volume fraction (\(\phi\)) and the average distance (\(r\)) varies linearly with their diameter according to the following equation:  
\[\langle r\rangle=d\left(\frac{\pi}{6\varnothing}\right)^{1/3} \tag{1}\]  
Accordingly, EMI increases linearly as a function of the particle volume; thus, indicating a strict correlation among the magneto-rheological response of the whole sample and the filler's volume, so that the switching effect increases by increasing the particles size.