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Edited by: Norman M. Wereley, University of Maryland, College Park, United States

Reviewed by: Xufeng Dong, Dalian University of Technology (DUT), China; Xiaomin Dong, Chongqing University, China

This article was submitted to Smart Materials, a section of the journal Frontiers in Materials

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

In this work, we propose mesoscopic model to investigate the surface micro structures of magnetorheological elastomers (MREs) under a magnetic field. By comparing the surface roughness changes of MREs, we found that the surface micro-deformation of MREs, not the field-induced hardness, mainly accounts for the controllable friction characteristics of MREs. The results also demonstrate that the field-induced friction of MREs depends on the particle contents as well as the initial surface roughness. The model predicts that the maximum relative roughness change of MREs occurs when the MRE has particle volume fraction of around 9%, which is validated by experimental results.

Polymers are hyperplastic materials that can be subjected to a large recoverable deformation under a relatively small loading. In taking advantage of this natural property, researchers have developed adaptive materials called magnetorheological elastomers (MREs), by embedding magnetic particles (micron size) in the polymer matrix (Jolly et al.,

Recently, several experimental studies (Lee et al.,

In fact, the surface micro-scale morphology may mainly contribute to the tribological characteristics of the MREs in a magnetic field. However, few studies (Gong et al.,

Although theoretical modeling of the deformation behavior of MREs has been studied by many others, these models originated from either the continuum mechanics (Dorfmann and Ogden,

Meanwhile, experimental studies have been performed to measure and analyze the deformation of MREs in magnetic fields. A testing platform with a CCD camera was established by Zrínyi et al. (

To fully understand how the external magnetic field affects the surface roughness of MRE, and how the initial roughness and particle volume fractions impact on the variation of the roughness, a 2 dimension mesoscopic model is proposed in this paper. By employing the Monte-Carlo method (Tsang et al.,

In the proposed model, we assume that the radius of magnetic particle sizes follow normal distribution, and the particles are tightly bonded to the matrix. In addition, the effect of polymer networks on particle interaction is negligible in the theoretical simulation (Davis,

Figure

The two dimension mesoscopic model of MRE.

Where _{n},_{n}) represents the coordinate of the _{j}) is the Fourier transform pair of _{n}), and can be expressed as:

Where _{j}) is the power spectral density of random surface profiles, and obeys gauss distribution function. And it can be expressed as follows:

Where _{cd} is the expectation of distance between two peaks of profiles.

In this work, we use parameter _{a} to describe the roughness of the MREs' surface micro profiles. It can be expressed as follows:

A sequential FEM^{25} is adopted in this paper to solve the magneto-mechanical coupling problem and obtain the micro deformation of MRE model in Figure _{i} on each particle surface ∂Ω_{i} can be calculated from the local field ^{M} as follow (Ly et al.,

Where _{i}, μ_{i}, μ_{0} is the permeability for the particles and matrix, respectively,

The simulation results of the MRE model under an applied magnetic field of 1,000 kA/m are shown in Figure

Simulation results with proposed model

Figure _{r} with initial surface roughness of MREs. The relative roughness change is defined as: _{r} = (_{m}-_{m}, is the roughness under a magnetic field, _{r}, When initial profile is smooth. And we can also explain it by an extreme assumption; we can imagine a MRE which has an absolute smooth surface that should become rough when superimposed on inhomogeneous deformation, which is the result of external magnetic loading.

Magnetic induced relative roughness _{r.}

Further, we investigate how the particle contents in MREs affect the relative roughness changes under the same applied magnetic field. We set the initial surface roughness of MREs to be 1.67 μm, and analyze the field-induced surface profiles for the MREs with different particle volume fractions. Figure

It can be seen that there is an optimal particle volume fraction for the relative roughness changes, in which the _{r} has the maximum absolute value. It is interesting to note that optimal particle volume fraction for the _{r} is around 9%, but is not 27%, in which the magnetorheological effect is predicted the strongest (Davis,

In this section, two kinds of isotropic MREs are manufactured by uniformly embedded magnetic particles into silicon rubber (HT-18; Shanghai Tongshuai Co., Ltd, China). As shown in Figure

MRE samples

Figure

White light interferometer test results of a typical MRE (10% particle volume fraction, generated by iron mold)

Comparisons of roughness of MREs for different particle volume fractions with/without magnetic field.

Figure

In summary, a mesoscopic model that considers deformation of surface micro-structures of MREs has been established to predict the surface roughness of MREs under magnetic fields. The model can explain how the field-induced friction of MRE changes as a function of particle contents, and how the initial surface roughness affects the changes. In addition, the proposed model has been verified experimentally. These findings may contribute to the area of interfacial friction control, in which controllable friction surfaces or techniques are expected to apply for the design of high efficient smart devices and mechanical systems.

RL and XL contribute the experimental parts of this works. XW gives some advises of this manuiscript and farbricates the MRE. SC writes the paper and establishes the surface model of MRE.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.