## 1. Introduction

Magneto-rheological elastomer (MRE) composites belong to the category of smart materials, showing a fast (milliseconds) and reversible transformation, including a controllable stiffness and frequency-dependent viscoelastic behavior, when subjected to a magnetic field [

1]. Such composites generally show variations in magneto-rheological (MR) effect for applying in magnetic flux densities of the order of magnitude of 0.8 T [

2]. The conventional use of MR fluids creates the settling of particles within the matrix as the function of time. To solve the issue of sedimentation of particles, MR elastomer emerges as an alternative polymer for the MRE composite [

3]. The properties could be influenced by the function of temperature.

Figure 1 is a schematic representation about the role of temperature for the transformation of MR fluids to elastomer [

4]. The MR effect in the composite opens a considerable property making them suitable for the application in mechanical systems where the active control of vibrations or transmission of torque are required. Such as in the areas of tunable vibration absorbers, shear type dampers, composite dampers, isolators, seismic vibration dampers, brakes, control valves, clutches, and artificial joints [

5,

6]. Furthermore, application fields using the magnetic control are those related with the thermal energy transfer, sound propagation, and isothermal magnetic advection, until you get to the biomedical applications [

7,

8]. Similarly, magnetic nanocomposites find important applications in the areas of remediation, catalysts, and microwave absorbers in response to external stimulus [

9]. In addition, other than elastomeric polymers, current research also focuses on biocompatible and thermoresponsive polymers in the fabrication of magnetic field responsive composites [

10].

Conventional MRE composites consist of two-phase matters obtained by dispersing magnetizable micron-sized solid particles in a liquid matrix, up to 30 vol %. Due to their considerable saturation magnetization (µ

_{0}M

_{s} = 2.1 T), iron and carbonyl iron particles are commonly used to this purpose, whilst silicone oils are employed as carrier liquids. Additives are necessary to inhibit sedimentation and aggregation of filler particles within the matrix, in addition, they provide lubricating properties [

11]. Silicone rubber, one of the most common elastomers, is used a as matrix consisting of two-phase liquids with base/binder in the 1:1 ratio. Generally, in the composites fabrication after the adding of the magnetic particles into the matrix, a curing is carried out either in the absence (isotropic MREs) or in the presence (anisotropic MREs) of an external magnetic field. The efficiency of the MRE composite, oxidative and chemical stability, and durability, strictly depends on various factors, among those, particles aggregation plays a key role, considering that the interface particles-matrix is determinant in the durability of the composite [

12,

13]. Thus, in designing MRE composites the main purpose is to obtain the highest MR effect, by inducing magnetization of the particles used as filler [

14]. In fact, when the magnetic field is not present, it is possible to observe a random distribution of the particles within the matrix; thus, leading to an isotropic composite. Differently, the presence of a magnetic field, during the preparation, leads to the particles magnetization and attracting one another along the field lines, with the formation of an anisotropic aggregate that spans the system. The so obtained composite shows high yield stress and a large shear rate-dependent apparent viscosity, with increase in viscoelasticity due to the applied magnetic field. The magnetically induced shape change, because of the MRE based magnetostrictive sensors, is very effective with relatively soft materials. This effect, the so-called magnetostriction effect, is due to the decrease of the deformation (ε) as a function of the inverse square root of the elasticity modulus (

E), (ε~

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 Mehnert 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.

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, 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 (

ф) and the average distance (

r) varies linearly with their diameter according to the following equation:

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.

#### 1.1. Physical Static Mechanism of MR Effect

Coupling the MR’s magnetization with the anisotropic interaction we obtain the “particle magnetization model”, which attributes the MR effect to the magnetic permeability mismatch among the constituent phases, both the continuous and dispersed one. Considering the solid phase as the magnetic one, it could be possible to observe that the larger size particles behave as magnetic multi-domains. Considering the particle’s magnetic moment is field-induced, their Brownian motion is neglectable; furthermore, the solvent thermal forces (∝ KT) are generally much smaller than magnetic and hydrodynamic ones.

A simplified model could have been achieved by neglecting multibody and multipole magneto static interactions among filler molecules. The magnetic moment of a particle with single domain and magnetizable sphere of radius, in a linear magnetization regime, is

where

μ_{0} is the permeability of the vacuum and is equal to

${\mu}_{0}=4\pi \times {10}^{-7}{T}_{m}{A}^{-1},$μ _{cr} is the relative permeability of the continuous phase, and

β is the contrast factor or coupling parameter

β =

${\mu}_{pr}-{\mu}_{cr}/{\mu}_{pr}+2{\mu}_{cr}$,

μ_{pr} is the relative permeability of the particles, and

H_{0} is the magnetic field strength. Contrariwise, at higher magnitude, the particle magnetization saturates and the magnetic moment becomes independent of the field strength:

In a linear regime, the interaction energy’s magnitude between two magnetic moments is

where 0 < β < 1 for strong MR fields (conventional conformation), and

$-0.5<\beta <0$ for weak MR fields (not conventional conformation). The magnetostatic particles interaction dominates overall thermal motion in case of chain-like particle aggregates. The particles movement within the elastomer during fabrication of MRE composite results in kinetic aggregations into two different regimes. Firstly, the aggregates average length increases as a power law, then single width chain-like structure laterally aggregate forming columnar structures. Thermal fluctuations of particles in position correlate to their mechanism of lateral aggregation. Iron particles based MRE composite show coarsening defect of tip-to-tip stage of aggregation, leading to a local variation in the magnetic field surrounding to the chain-like structure. The lateral interactions between dipolar chains play an important role in the isotropic structure of MRE samples. In the MREs, the elastomer shows steady shear flow, as a result, the Mason number (

M_{n}), is basically dimensionless; thus, shear rate can be defined as the ratio between the hydrodynamic drag and the magnetostatic forces (estimated as the dipole force magnitude) acting on the particles [

16].

η_{c} is the continuous phase viscosity and

$\dot{\gamma}$ is the magnitude of the shear rate tensor. MR vulcanized elastomer behave as Newtonian fluids in the absence of a magnetic field, whilst if a magnetic field is applied transverse to the direction of flow, it is possible to observe a yielding, shear, and viscoelastic behavior.

Yield stress is based on macroscopic and microscopic models. Macroscopic models employ minimum magnetic energy distribution that leads to homogenous structures of MRE composite reinforced with fillers such as spherical or layered particles in aggregates. This model contributes towards shear anisotropy of the strained aggregates under small deformation. Contrariwise, microscopic models treat inter-particle interactions, such as single particle chains sheared under an external magnetic field. The particle’s magnetostatic interactions dominate the shear stress, and shear-induced deformation is assumed to be affine; thus, the magnetic field strengthens the network without affecting its shape significantly. Micro mechanical chain-like models are based on the balancing of magnetostatic and hydrodynamic forces. MRE system shows linear viscoelasticity when subjected to small strains. Instead, high order harmonics define the critical strain; thus, sanctioning the transition from the linear to the non-linear viscoelastic regime. Then, larger strain amplitudes define the second critical strain with a transition from the nonlinear viscoelasticity to viscoplasticity. In the presence of a magnetic field, and thus of a field-induced structure, it is possible to observe a storage modulus (G′), generally of an order of magnitude greater of the loss modulus (G″). At completely saturation of the particles magnetization, in the presence of a large field strength, G′ is independent by this field strength, G′ = 0.3 фµ_{0}M_{s}^{2}.

#### 1.2. Dynamic of MRE

Dynamics of MRE are considered from the shear deformation for a linear viscoelastic material. The dynamic behavior is represented with a complex modulus related to the vibration frequency and controllable by external magnetic fields. The dynamic model or MRE’s constitutive relationship [

17] is given by

where

τ and

γ represent the MRE’s shear stress and strain, respectively;

a_{i} and

b_{k} are the constant coefficients dependent on external magnetic field strength; and

n_{1} and

n_{2} are integers. Considering the periodic harmonic strain and stress, the equation becomes

where

$\stackrel{\mathsf{=}}{\tau}=\overline{\gamma}{e}^{j\omega t}$,

$\tau =\overline{\tau}{e}^{j\left(\omega t-\theta \right)}$, with

$\overline{\gamma}$ and

$\overline{\tau}$ being amplitudes of stress and strain, respectively.

$j=\sqrt{-1}$, ω is the vibration frequency,

θ is the delayed phase between stress and strain, and

G(jω) is a complex modulus that is a function of vibration frequency

ω and MRE’s external magnetic field strength. The real part of the complex modulus

${G}^{R}\left(\omega \right)$ is the storage modulus representing the viscoelastic stiffness. The imaginary part

${G}^{I}\left(\omega \right)$ is the loss modulus, with the ratio of loss to storage modulus, represented by the loss factor, describing the viscoelastic damping:

The differential equation in Equation (6) is very difficult to solve for MRE systems. Therefore, the Equation (7) is commonly used to describe the MRE’s dynamic stress–strain relationship. Experimental evidence shows mostly a linear increase of the storage modulus as a function of the vibration frequency, and both the storage and the loss modulus linearly increase with the external magnetic field strength in a certain range. Hence, the storage modulus

${G}^{R}\left(\omega \right)$ and the loss factor Δ(ω) can be expressed approximately by:

with

${\alpha}_{0}$,

${\alpha}_{1}$ and

${\beta}_{0}$ depending only by the applied magnetic field strength.

## 2. Materials and Methods

We take into consideration a MRE composite prepared by mixing 30 vol % of iron and carbonyl iron particles in silicon elastomer matrix [

18]. This latter was prepared from the combination of matrix/binder in the ratio of 50:50 in quantity. The iron particles incorporated into silicon elastomer had a size of 50–100 µm and purity > 95%. The used matrix was obtained by polyaddition, ZA 22, and by polycondensation, N 1522. The carbonyl iron was only considered in the matrix of ZA 22 (

Figure 3).

In order to improve the particle’s adhesion on the matrix surface, we used silicon oil. Therefore, particles treated with silicon oil, matrix, binder, and catalyst were slowly stirred, at room temperature, until homogenization (ca. 30 min). The obtained mixture was then treated under vacuum for removing air bubbles and then cured in the standard mold (ca. 24 h), without any influence of the magnetic field. Cylindrically samples were designed, with a length of 20 mm and a radius of 5 mm. The anisotropic composites were prepared using magnetic field along the perpendicular direction of the sample during curing time (

Figure 4) [

18].

The induced magnetic field was applied perpendicularly to the sample thickness during the static and compressive mode. However, the closed domain of the magnetic field was applied parallel to the sample position during shear or dynamic mode. Therefore, both the magnetic intensity and the sample orientation in the magnetic field have been set up. As shown in

Figure 5, the MRE composite was put in contact with the copper slabs of the magnetic field circuit, both with its upper and lower surface. The simulation was performed by the means of MSC MARC, non-linear dynamics Software (Newport Beach, CA, USA). The simulation parameters were carried out at the boundary conditions of the magnetic potential and current of 1 A. After this test, SEM and µCT analyses were carried out on the MRE composites.

A Hitachi TM-3000 (Hitachi High-Technologies Corporation, Tokyo, Japan) with a secondary electron detector and field emission source was used to perform scanning electron microscopy. Sample fragments were assembled on aluminum stubs, out-gassed in a desiccator (ca 48 h), and then coated with a 4 nm layer of platinum before SEM imaging. An acceleration voltage of 10 kV was used in SEM analyses. The µCT analysis was carried out, in sky scan mode with 3D reconstructed images from slices of the two-dimensional structure, on an open tube source with Tungsten (Bruker, R.M.I. s.r.o., Lázně Bohdaneč, Czech Republic). The instrument setting and the measurement parameters are reported elsewhere [

20,

21,

22]. Various modes of operation of magneto rheological elastomeric composite are tested in static, compressive (deformed), and dynamic (shear mode), to observe the effect of various magnetic flux density and the hysteresis behavior from force versus displacement response. Static and dynamic properties of MREs composite, of isotropic and anisotropic filler distribution, were investigated as a function of the magnetic intensity, frequency, strain amplitude, and damping properties in various modes [

23]. The schematic diagram of the static and compressive (deformed mode) is shown in

Figure 5 and

Figure 6.

## 4. Future Prospectus on the Applications of MREs Composite

MRE composites have opportunities in the field of elastomer devices in practical way of engineering applications. MRE composites under tension, compression, and shear test shows possible uses in the application areas of vibration isolation and absorption capacities. Combined approach of shear and compression test may allow application in the area of sensing of elastomer devices. MR elastomer devices include large adaptive working frequency range, low power consumption, and compact configuration. Thus, given a sufficient magnetic field is provided, devices with large changes in their modulus and damping (i.e., MR effect), between field-on and field-off status, can offer a great adaptive range. Effect of filler size, shape, and nature of the matrix has a significant role in the quality of MREs composite. The volume fraction of 30% of filler particles are considered to be optimized for significant distribution of fillers within the matrix. The circular and smaller particles such as carbonyl iron with higher magnetization contribute maximum MR effect in the MREs composite. Soft elastomer matrix such as rubber matrix could be considered as a most suitable one; however, the vulcanization time is longer that may hinder the durability of the devices.

Several cross-linking systems such as sulfurs, organic peroxide, phenolic resins, amino acids, ultrasonic waves, and microwaves have been used for the rubber vulcanization. Among these sulfur and peroxides are the most widely used in the vulcanization process. The mechanism of the accelerated sulfur vulcanization is still controversial partly due to the complexity of the formulation. Therefore, the need to consider the trade-off among MR effects and other performance criteria should be carefully considered for these elastomers. Their application in civil engineering structures, especially for base isolation systems, has recently attracted increasing attention towards adaptive base isolators made of MREs composite.

A decrease in the storage modulus as a function of the strain increase, when the filler network is subject to a breakdown, the so-called Payne effect, is shown by all MRE composites, some by more and some by less. In particular, the isotropic MREs show, at low particles content, a systematic decrease in the small-strain storage modulus G′ [

38,

39]. By contrast, an increase of the small-strain storage modulus

G′ is generally recorded for the anisotropic MREs. With 30% particle content, anisotropic MRE composite change was more pronounced for the storage modulus (20.4%) than for the loss modulus (8.8%), both changes were determined at 30 Hz with the maximum applied magnetic field being about 0.775 T. This behavior is explained with the magnetized particle arrangement in anisotropic strings during the curing process. The new arrangement that contributes to the stiffness of the compound. Just the micro-sized iron particles, with high saturation magnetization, show a considerable orientation effect within a magnetic field. In fact, due to their large magnetic moment, they generate strong attractive dipole–dipole interactions when the magnetic field is applied [

40,

41]. Furthermore, close contact is also decisive to get these dipole–dipole interactions in the magnetic field [

42]. MRE’s devices are generally classified into two categories, those having either fixed poles (pressure-driven mode) and those having relatively moveable poles (direct-shear mode and squeeze-film mode). The first category includes servo-valves, dampers, and shock absorbers, whilst the second one includes clutches, brakes, chucking, and locking devices. A third mode of operation, also known as biaxial elongation flow mode, appears in slow motion and/or high force applications.