Microstructural characterization and effective viscoelastic behavior of magnetorheological elastomers with varying acetone contents

Abstract

Magnetorheological elastomers (MREs), a class of polymer-based composites with dispersed ferromagnetic micro-particles, fall in the class of smart materials, because their macroscopic or effective rheological properties can be continuously, rapidly, and reversibly changed with the application of a magnetic field. Conventional magnetorheological elastomers exhibit poor mechanical properties and magnetorheological effect as a result of their matrix materials and the particle-matrix interfaces. Here, we investigate the effect of acetone contents on the magnetorheological elastomer microstructure at the interfacial regions using the scanning electron microscope and the three-dimensional nano-CT imaging, as well as determining the overall or effective mechanical properties of magnetorheological elastomers. It is shown that acetone increases both the overall storage modulus and loss factor along with the magnetorheological effect due to acetone’s reaction on the interface as well as its effect on iron particle alignment.

Keywords

Magnetorheological elastomer composites interface acetone dynamic mechanical analysis microstructural characterization

Introduction

Magnetorheological (MR) materials are in the category of smart materials since their mechanical properties can be rapidly and reversibly changed with the application of an external magnetic field (Carlson and Jolly, 2000). These materials consist of micron sized ferromagnetic particles which are suspended in a nonmagnetic matrix. Typically, iron particles are used as it contains one of the highest saturation magnetization of known materials (Davis, 1999). Since the discovery of the MR effect by Rabinow (1948), three primary classes of magnetorheological materials now exist: MR fluids, MR foams, and MR elastomers (Jolly et al., 1996). These materials can be used in many different applications such as seismic dampers in buildings, shock absorbers in vehicles, and MR structures in prosthetics (Ginder et al., 1999; Jolly et al., 1996).

Magnetorheological elastomers (MREs) can exhibit either isotropic or anisotropic properties (Ginder et al., 1999; Li and Sun, 2013b). Inferred by the name, isotropic MREs behave as an isotropic material due to its randomly distributed particles. Anisotropic MREs consist of aligned iron particles which results in the direction of applied magnetic field within the rubber matrix (Yin and Sun, 2005). In order to produce these chain-like structures, a magnetic field is applied to the composite during the crosslinking step of the matrix so that the columnar structures can form and become locked in place upon final cure (Li and Sun, 2011). Because chains are aligned in one direction, the rheological and mechanical properties behave differently depending on the orientation of MREs. While still primitive in knowledge when compared to the original MR materials, MREs offer many advantages in comparison with MR fluids. One of the most attractive incentives for the use of MREs over MR fluids is due to the fact that MRE’s iron particles are fixated within the matrix. On the other hand, due to MR fluid’s liquid matrix, the iron particles tend to settle over time. Furthermore, MR fluids are in the liquid state, needing to be contained whereas the MREs are in the solid-state region, already dimensionally fixated (Böse et al., 2012).

While taking great strides in improving over MR fluids, MREs have challenges in terms of their mechanical performance. First, because of the inclusion of a matrix that is generally rubber (e.g., silicone rubber, natural rubber, and polybutadiene), the MRE’s initial stiffness is not high enough to be used in certain applications (Luo, 2015; Pan and Zhong, 2016). A simple method of eradicating such low initial modulus is by using a stiffer matrix; however, the damping properties may be compromised due to the matrix’s inability to dissipate energy at the high rate that soft elastomers allow. Additionally, in an effort to improve initial mechanical performance of the elastomer, the MRE would be exposed to a magnetic field during the curing process (the last step of fabrication processes). However, perfect alignment of the iron particles is not possible as a high magnetic field will still be unable to completely align the iron particles along the direction of applied magnetic field (Borbáth et al., 2012; Gundermann et al., 2013; Günther et al., 2012). Second, the MR effect of MREs may not have a high enough range to function as a material in a system. The limitation arises as a result of the saturation magnetization that iron (or any ferromagnetic particle) holds. Furthermore, high magnetic fields applied in field application may be deemed difficult to achieve.

The aforementioned challenges that are related with the use of MREs lead to the research in this article. Because the mechanical properties of iron particles and those of the matrix are inherently fixed, the major improvement that can arise from inserting additives to the MRE results into a change in the interface regime between the matrix and the particle. With the limited compatibility, the interaction between the iron particles and matrix can be either strong or weak depending on additives included in MREs. As a result, the rheological and mechanical performance of MREs may be altered (Leblanc, 2002; Stepanov et al., 2007). In an effort to improve the initial mechanical properties as well as strengthen the MR effect of the elastomer, acetone is introduced within the MREs. By adding acetone in the system, the acetone can “wet” the iron particles thereby drastically reducing the bonding occurring between iron particles and the silicone matrix. By doing so, the iron particles align better within the elastomer when exposed to a magnetic field due to the fewer interfacial bonds. Additionally, acetone’s introduction in the system lower the silicone’s initial viscosity thereby allowing for better alignment or orientation which results in higher mechanical properties. Furthermore, MR effect increases as the overall magnetostriction increases. Along with higher stiffness, the lack of connections also results in a higher loss factor as interfacial friction between the iron particles and the matrix increases. Experimental exploration occurs with both isotropic and anisotropic MRE through single-lap shear testing. In an effort to understand how MR elastomers are affected by the fabrication processes, research is done in characterizing the composition of elastomers. The orientation of iron particles, which are ellipsoidal in shape, is determined through three-dimensional (3D) X-ray imaging, providing insight to the effectiveness of an applied magnetic field during the curing process. Also, the microstructural interface of samples with and without acetone is analyzed through the use of a scanning electron microscope (SEM).

Materials synthesis and fabrication

In an effort to properly analyze the effect that acetone has on the MR elastomer, shear silicone samples with varying acetone percentage were produced to ascertain acetone’s effect on the matrix. The reason that shear tests were designed is because the shear moduli of the MR elastomer is typically more sensitive to the applied magnetic field (Davis, 1999). Furthermore, both anisotropic and isotropic MRE samples containing 22.75% iron particles by volume were prepared. Lastly, an anisotropic MRE sample containing 10.00% iron particles by volume was prepared exclusively for nano-CT imaging. The materials used were a two-component room-temperature vulcanizing silicone rubber (Sylgard 182 by Dow Corning Corp., base and curing agent), 325 mesh pure iron particles (type I-1021 by Materion), and certified ACS Acetone (A18-500 by Fisher Scientific). For the silicone samples, ten parts of silicone rubber base and one part of curing agent were first mixed with a certain acetone weight percent (wt%), which was then blended for five minutes with a high-speed stirrer. MRE samples follow the same format, except that iron particles were included with base and curing agent and then mixed. The samples were then subsequently vacuumed for roughly 15 minutes in a desiccator (with a maximum time of 20 minutes used), at which point the sample no longer noticeably degassed. The samples were then poured in rectangular molds that that were 25.4 mm by 12.7 mm by 3.175 mm thick. For samples labeled anisotropic, two permanent magnets (0.35 T) were placed between the molds as the samples cured. Throughout the fabrication processes, samples were minimally exposed to ambient air and vacuum in order to reduce the loss of acetone through evaporation; samples were exposed to a maximum of 20 minutes in a desiccator during the fabrication as to avoid acetone evaporation, and samples were poured and sealed (with and without an applied magnetic field) within an hour of initial mixing. The curing time for the samples was approximately 24 hours. After the curing process, samples were then subsequently super glued between two aluminum plates for dynamic testing.

Microstructural characterization

SEM imaging

Studies involving interface models with a mathematical framework of imperfect interfaces have been formulated in the literature (Hasebe and Yamamoto, 2015; Hashin, 1990; Li and Sun, 2013; Liu et al., 2006; Paulino et al., 2006; Yanase and Ju, 2014; Yao and Huang, 2014; Shen and Shao, 2015). Particularly, a micromechanics-based progressive damage model (Liu et al., 2006) of particle-filled composites was studied to take into account the particle-matrix interfacial debonding. Further investigation (Li and Sun, 2013a) was conducted for modeling the effective viscoelastic properties of nanocomposites filled with carbon nanotubes with consideration of imperfect interfacial condition between the filler and matrix as well as the concentration and aspect ratio of fillers. Similar to the previous work, the imaging obtained through SEM in this article exhibits the weakened interface classically seen with conventional MREs. Figures 1 and 2 display the SEM images of isotropic MRE samples with 0 and 1.0 wt% of acetone, respectively. It is shown that the MRE sample with acetone has drastically lower amount of connections in the interface area. This is because acetone’s wetting effect inhibits the bonding between iron particles and the surrounding matrix; therefore, the iron particles with acetone in the system are more susceptible to magnetostriction when compared to its conventional counterpart (Ginder et al., 2002).

Figure 3 further shows the SEM images of isotropic MRE and anisotropic MRE at approximately 300× magnification, from which it can be seen that the MREs contain micro voids within the silicone matrix, and surrounding the iron particles. Furthermore, it can be seen that no clear chain network exists in the direction of applied magnetic field for the anisotropic samples; the high proportion of iron along with its abnormal shape in the system may impede seeing the individual chain-like structures in the direction of applied magnetic field. As a result of a lack of the chain, a new method in determining alignment will next be used through the 3D tomographic visualization of the samples. Quantitative results will then be extracted through post-processing of the 3D images. These results are presented in the following subsection.

3D X-ray tomography

Because the alignment is not clearly visible in the anisotropic MRE samples, a nano-CT modality (Xradia/Zeiss Versa XRM 410) is employed for the anisotropic MRE samples. Figure 4 displays the 3D representation obtained though nano-CT modality for anisotropic MRE samples with two particle concentrations. The chain alignment is clearly visible for anisotropic MREs with 10% iron particles. However, similar to the SEM images, MRE samples with 22.75% display no clear sign of alignment through 3D imaging.

While previous efforts (Borbáth et al., 2012; Gundermann et al., 2013; Günther et al., 2012) have used 3D imaging to quantify MREs, such as determining the micro-movement of particles as a result of a magnetic field, the usage of 3D imaging as a means of quantifying orientation has yet to be tested. To determine the orientation of the iron particles, a post-processing software (Avizo Fire 8.1 by VSG FEI) is used to quantify the images obtained from 3D imaging. To begin the process, the elastomer is first removed by eliminating the lower portion of density until only the iron particles are left. Afterwards, each iron particle is given a separate label, as can be seen in Figure 5.

Based on the initial SEM images, the iron particle’s average size is roughly around 15 × 35 × 50 microns (ellipsoidal shaped), which results in an average volume of 26,250 micron cubed. As can be seen from the quantitative results obtained, the volume of each iron particle is rather close to the original estimation that was determined through SEM and from 3D imaging; furthermore, the average obtained iron size between various nano-CT scans of different samples imaged are nearly identical. This would indicate further that the removal of the lower portion of density and the labeling of each individual particle with the quantitative analysis tool is rather accurate. With the labeling of each particle, the longest section of each ellipsoidal iron particle is then resolved and the average orientation of the particles is determined (Table 1). The results indicate that the orientation of the iron particles with a magnetic field applied is around 66 degrees. The slight difference of angles (66.46° vs. 65.42°) that arises between the varying iron volume percent MRE samples may be due to the higher resistance placed on the MRE with higher percentage of iron particles (22.75%). This results in a slightly lower particle orientation when compared to 10% MRE shown in Table 1. Based on the results, while the characteristic chaining of iron particles is not visible, the re-orientation of the iron particles at the micro-scale displays the anisotropy (specifically transverse isotropy) that arose from the applied magnetic field during the curing process (Nezhad et al., 2016; Nguyen and Dormieux, 2016). It should be noted that that the effect of an applied magnetic field in this case only allows for slight particle alignment when compared to isotropic MRE samples, which is listed in the following section.

Table 1.

Postprocessing results for aligned MRE samples.

Sample	Avg. vol of particle (µm³)— postprocessing results	Avg. vol of particle (µm³)— SEM imaging	% Actual vol of particles	% Avizo vol of particles	Average particle orientation
Anisotropic 10.00% MRE	28,792	26,250	10.00	9.73	66.46°
Anisotropic 22.75% MRE	27,111	26,250	22.75	22.65	65.42°

In order to resolve how applied magnetic fields and acetone implementation alters orientation, three samples are imaged with the nano-CT: (1) 22.75% iron particles by volume isotropic MRE with 0 wt% acetone; (2) 22.75% iron particles by volume anisotropic MRE with 0 wt% acetone; and (3) 22.75% iron particles by volume anisotropic MRE with 1.0 wt% acetone. For these samples, the magnetic field applied during the curing process was slightly decreased (0.25 T). Similar to the previous case, the MRE samples are post-processed, and the results of iron particle orientation are displayed in Table 2. Sample 1 has average particle orientation of 56.33°; when compared to the theoretical average of random particles at 57.30°, the isotropic sample displays nearly perfectly random orientation distribution (Sun and Ju, 2005). When comparing the second and third samples, it can be noted that the sample with acetone integrated within the MRE has a slightly higher orientation. This indicates that the acetone plays a role in aiding the orientation of the iron particles when an applied magnetic field is placed on the sample during the curing process. Because acetone has the capability of preventing iron-silicone attachment, the MRE samples are able to re-orient more during the curing process. Furthermore, when comparing anisotropic sample with 22.75% iron that was cured under 0.35 T magnetic field (Table 1) with the sample cured with 0.25 T magnetic field (Table 2) with no acetone, higher magnetic fields resulted in higher orientation.

Table 2.

Average particle orientation for MRE samples.

Sample	Average particle orientation	Relative increase with respect to isotropic MRE
Isotropic MRE 22.75% iron	56.33°	—
Anisotropic MRE 22.75% iron with 0 wt% acetone	61.14°	8.54%
Anisotropic MRE 22.75% iron with 1.0 wt% acetone	62.31°	10.62%

Dynamic mechanical analysis

The overall or effective viscoelastic properties of MREs are determined using the dynamic mechanical analysis (DMA) via a Bose Electroforce 3200 system. External magnetic fields are placed perpendicular in direction to the applied shear force for shear testing. For anisotropic MREs, the applied magnetic field is applied parallel to the chains of iron particles in the elastomer. For the shear test, a permanent magnet with rectangular pole areas and adjustable pole spacing is used. By adjusting the spacing between the magnets, 0.1 and 0.2 T flux density outputs are used on the samples. Because the samples produced are small in size compared to the magnets used during DMA, the magnetic fields are almost uniform throughout the shear samples. Figure 6 shows the testing configuration for shear samples.

Silicone matrix samples

The frequency scans of small-strain storage moduli along with the loss factors for silicone, with and without applied magnetic field during curing, under shear loadings are shown in Figures 7 and 8. The samples are tested at room temperature with amplitude of 0.5%. The frequency ranges from 0.1 to 100 Hz, with external magnetic fields applied during testing from 0 to 0.2 T. The figures represent the storage modulus and loss factor of silicone matrix with differing acetone percentages used during fabrication. Four differing levels of acetone are produced: 0, 0.5, 1.0, and 2.0 wt%. For the case of 2.0% acetone, the material lost its mechanical integrity; therefore, the results were omitted. Two sets of each sample are produced, one with a magnetic field applied during the fabrication processes and the other without. This is done to properly assess the effects a magnetic field has on a nonmagnetic material. Two samples were produced for each composition, and averaged, in an effort to realize fabrication errors and resolve them.

As can be easily noted, the applied magnetic field during the testing process has no effect on the dynamic properties of the sample; samples of the same of composition with differing magnetic fields during the testing process have results that completely overlap. Furthermore, the applied magnetic-field during the curing process has no effect on the sample’s properties. From the DMA results, there are some slight differences in modulus and loss factor between silicone samples that are exposed to a magnetic field during the curing process and that that was not; however, such slight differences are directly dependent on the slight variation that naturally occurs between sample production, testing temperature, and so forth of each sample. From the results, it is indicative that the magnetic field does not affect silicone or acetone. From Figures 7 and 8, it can be observed that the shear modulus for silicone with and without applied magnetic field during fabrication decreases with increasing acetone percentage. This is due to the fact that the acetone does not intermix within the silicone sample. Because of this, the acetone’s liquid state results in a lower shear modulus as acetone cannot take shear loading. As a result of the lower initial modulus, the loss factor increases with higher acetone percentage. As can be observed from the DMA results, the storage modulus and the loss factor increase with increasing frequency. This is related due to the viscoelastic nature of the silicone used within the elastomer.

MRE samples

The frequency scans of small-strain storage moduli along with the loss factors for both anisotropic MREs and isotropic MREs under shear loadings are shown in Figures 9 and 10. Similar to the silicone samples, the MRE samples are tested with a frequency that ranged from 0.1 to 100 Hz, with amplitude of 0.5%, and at room temperature. Four differing levels of acetone were used: 0, 0.5, 1.0, and 2.0 wt%. MRE samples with a composition of 2.0% acetone were fabricated, however, the elastomer lost its structural integrity. Because of this, the results are not included in the figures. Each representation of the MRE’s results is obtained through the averaging of two samples with identical material composition, which is done in an effort to minimize fabrication errors and/or outliers from being obtained during the DMA.

It can be observed from Figure 9 that for the isotropic MRE containing 0.5% of acetone has higher initial shear modulus followed by 0% and 1.0%, respectively. For the anisotropic MRE, as can be seen in Figure 10, it is determined that 1.0% of acetone within the MRE results in the highest initial storage modulus, followed by 0.5% and 0%, respectively. As acetone is incorporated into the matrix during the initial mixing, the viscosity and yield stress of the pre-cured mix is drastically lowered, thus allowing voids present in the matrix to be more effectively removed during the vacuuming process (noted in Figure 3). The reasoning as to why anisotropic MREs would need a higher weight percent of acetone compared to its isotropic counterpart may be a result of the clustering of the iron particles that occurs in anisotropic samples. The clustering of iron particles results in a higher percentage of voids when compared to conventional isotropic MREs (Borbáth et al., 2012; Günther et al., 2012). Furthermore, when a magnetic field is applied during curing, the movement, and re-orientation of iron particles may result in precipitation of voids. With 1.0% acetone in the isotropic sample, there is an oversaturation of acetone which, similar to the silicone samples, decreases the shear modulus of the sample. When viewing the loss factor for both anisotropic and isotropic MREs, the MRE containing 1.0% of acetone had higher damping properties, followed by 0.5% and 0%, respectively. The reasoning behind this is that the acetone has a “wetting effect” in the interface of MREs. By lubricating the system during the fabrication processes, the silicone and the iron particles are inhibited further from creating a connection. As a result, there is a higher amount of friction that can occur at the interface, producing a higher loss factor. The storage modulus and the loss factor increase with increasing frequency. The reasoning behind this is related with the viscoelastic nature of the silicone used within the elastomer. The increase in loss factor with increasing frequency is influenced by the iron particles embedded within the matrix and is related to the restructuring of the particle network during dynamic deformation (Hashin, 1965; Schapery, 1967).

Shown in Figure 11 is the absolute MR effect for isotropic MREs with respect to storage modulus and loss factor, respectively. From the results obtained, it can be seen that with increased magnetic field during testing, the storage modulus along with the damping of the MRE increase (Shen et al., 2004). However, the change in shear modulus is not high because: (1) isotropic samples have lower MR effect and (2) the applied magnetic field during testing is limited to 0.2 T. It is also observed that the absolute MR effect is independent of the frequency applied, indicating that the linear viscoelastic properties of the silicone are active within the system. The relative MR effect for the shear modulus of the isotropic MRE gradually decreases with increasing frequency due to the higher initial shear modulus with higher frequency. The absolute MR effect for loss factor gradually decreases to zero with higher frequency because higher frequency results in inability of the system to recover from the oscillation.

When comparing the absolute MR effect with the differing acetone levels, it can be seen that as the acetone weight percent increases, the absolute MR effect also increases. Because the acetone has a wetting effect on the iron particle, thus inhibiting the bond formation between the iron particles and silicone matrix, the iron particles are more capable of reorienting with an applied magnetic field. As a result, the iron particles are able to form stronger dipole-to-dipole bonds due to their closer interaction. With the addition of acetone the absolute change in damping increases when comparing values with the same applied magnetic field. Because the amount of connection between the iron particles and the silicone is lowered, the iron particles are allowed to displace and rotate a higher amount, resulting in a higher loss of energy due to the friction that occurs between the movement of the ferromagnetic particles and its surrounding matrix.

The frequency scans of the small-strain MR effect for anisotropic MREs are presented in Figure 12. As can be observed, the absolute MR effect for the aligned MREs is substantially higher than that of isotropic MREs. Since the aligned MREs are closer together in direction of the applied field due to clustering and the formation of chains within the elastomer, the dipole-dipole interactions are higher than that of isotropic MRE. When compared to the isotropic case, the anisotropic MRE also have higher MR effect when related to the damping of the system. As a result of higher dipole-dipole interactions in anisotropic MREs, the iron particles are applying a higher normal force on the silicone, causing a higher friction energy loss when dynamic deformation occurs.

From the DMA results, it can be observed that the MR effect related to the shear modulus of MREs with acetone is higher when compared to the case of the MRE with no acetone implemented during the fabrication processes. Similar to the isotropic case, since the acetone creates a wetting effect around the iron particles, the connection between iron and silicone is limited due to this effect. As a result, the iron particles are more able to move within the elastomer, thus allowing stronger dipole-to-dipole interactions to occur.

Conclusions

This article is devoted to the investigations of the microstructural characterization and effective DMA of MREs with varying acetone concentrations. The mechanical properties of each MR elastomer are determined, and the characterization of each elastomer’s composition is done through SEM and 3D X-ray tomography modality. The conclusions are drawn below, followed by suggestions on future work that may be done.

With relation to the dynamic viscoelastic properties of MR elastomers constructed, it is determined that samples produced with the inclusion of acetone showed an improvement on the zero-field shear modulus and loss factor, and the MR effect with relation to both the shear modulus and loss factor. This is due to acetone’s wetting effect on the iron particles during the curing process. Future research can be determined with MREs with higher magnetic fields during the testing procedure. The full capabilities of an MR elastomer will make it easier to determine where its implementation will be successful.

The use of nondestructive 3D imaging is tested as a means of determining orientation for anisotropic samples. The results indicated that not only does three-dimensional imaging offer the same results as SEM imaging in terms realizing alignment, but it also offers quantitative results that can be used for finite element analysis in the future. Because nano-CT imaging produces 3D microstructural images of materials, the following step includes creating a mesh of the elastomer. The elastomer may then be modeled, and the effects of force transformation through the system can be computationally determined. Furthermore, magnetostrictive effect as a result of an applied magnetic field can be determined through 3D imaging.

Footnotes

Acknowledgments

The support of the National Science Foundation is gratefully acknowledged. The authors gratefully acknowledge technical assistance from Dr Yu Wang, Dr Yongxue Li, and Ms Susana Anacleto of University of California Irvine in regards to SEM and nano-CT observations.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was sponsored by the National Science Foundation (NSF) under Grants No. CMMI-0800417 and CMMI-1229405.

References

Borbáth

Günther

Borin

(2012) XμCT analysis of magnetic field-induced phase transitions in magnetorheological elastomers. Smart Materials and Structures 21: 105018-1–7.

Böse

Rabindranath

Ehrlich

(2012) Soft magnetorheological elastomers as new actuators for valves. Journal of Intelligent Material Systems and Structures 23: 989–994.

Carlson

Jolly

(2000) MR fluid, foam and elastomer devices. Mechatronics 10: 555–569.

Davis

(1999) Model of magnetorheological elastomers. Journal of Applied Physics 85: 3348–3351.

Ginder

Clark

Schlotter

(2002) Magnetostrictive phenomena in magnetorheological elastomers. International Journal of Modern Physics 16: 2412–2418.

Ginder

Nichols

Elie

(1999) Magnetorheological elastomers: Properties and applications. Proceedings of SPIE Smart Structures and Materials 3675: 131–138.

Gundermann

Günther

Borin

(2013) A comparison between micro- and macro-structure of magnetoactive composites. Journal of Physics 412: 1–6.

Günther

Borin

Günther

(2012) X-ray micro-tomographic characterization of field-structured magnetorheological elastomers. Smart Materials and Structures 21: 015005–1–7.

Hasebe

Yamamoto

(2015) A crack initiation and two debondings development at the interface of a circular rigid inclusion under uniform loading. International Journal of Damage Mechanics 24: 965–982.

10.

Hashin

(1965) Viscoelastic behavior of heterogeneous media. Journal of Applied Mechanics 32: 630–636.

11.

Hashin

(1990) Thermoelastic properties of fiber composites with imperfect interface. Mechanics of Materials 8: 333–348.

12.

Jolly

Carlson

Munoz

(1996) A model of the behaviour of magnetorheological materials. Smart Materials Structures 5: 607–614.

13.

Leblanc

(2002) Rubber-filler interactions and rheological properties in filled compounds. Progress in Polymer Science 27: 627–687.

14.

Sun

(2011) Dynamic mechanical behavior of magnetorheological nanocomposites filled with carbon nanotubes. Applied Physics Letters 99: 131912-1–3.

15.

Sun

(2013a) A micromechanics-based viscoelastic model for nanocomposites with imperfect interface. International Journal of Damage Mechanics 22: 967–981.

16.

Sun

(2013b) Viscoelastic responses of silicone-rubber-based magnetorheological elastomers under compressive and shear loadings. Journal of Engineering Materials and Technology 135: 021008-1-7, .

17.

Liu

Sun

(2006) Elastoplastic modeling of progressive interfacial debonding for particle-reinforced metal-matrix composites. Acta Mechanica 181: 1–17.

18.

Luo

(2015) Mullins damage effect on rubber products with residual strain. International Journal of Damage Mechanics 24: 153–167.

19.

Nezhad

Zhu

. A simplified multiscale damage model for the transversely isotropic shale rocks under tensile loading. International Journal of Damage Mechanics. 2016. DOI:10.1177/1056789516639531.

20.

Nguyen

Dormieux

(2016) Viscoelastic properties of transversely isotropic micro-cracked materials. International Journal of Damage Mechanics 25: 141–152.

21.

Pan

Zhong

. Modeling the Mullins effect of rubber-like materials. International Journal of Damage Mechanics. 2016. DOI:10.1177/1056789516635728.

22.

Paulino

Yin

Sun

(2006) Micromechanics-based interfacial debonding model for damage of functionally graded materials with particle interactions. International Journal of Damage Mechanics 15: 267–288.

23.

Rabinow

(1948) The magnetic fluid clutch. AIEE Transactions 67: 1308–1315.

24.

Schapery

(1967) Stress analysis of viscoelastic composite materials. Journal of Composite Materials 1: 228–267.

25.

Shen

Shao

(2015) A micro–macro model for porous geomaterials with inclusion debonding. International Journal of Damage Mechanics 24: 1026–1046.

26.

Shen

Golnaraghi

Heppler

(2004) Experimental research and modeling of magnetorheological elastomers. Journal of Intelligent Material Systems and Structures 15: 27–35.

27.

Stepanov

Abramchuk

Grishin

(2007) Effect of a homogenous magnetic field on the viscoelastic behavior of magnetic elastomers. Polymer 48: 488–495.

28.

Sun

(2005) Elastoplastic modeling of metal matrix composites containing randomly located and oriented spheroidal particles. Journal of Applied Mechanics 71: 774–785.

29.

Yanase

(2014) Overall elastoplastic damage responses of spherical particle-reinforced composites containing imperfect interfaces. International Journal of Damage Mechanics 23: 411–429.

30.

Yao

Huang

Z-M

(2014) Stress concentration factors in the matrix with different imperfect interfaces. International Journal of Damage Mechanics 23: 745–771.

31.

Yin

Sun

(2005) Magnetoelasticity of chain-structured ferromagnetic composites. Applied Physics Letters 86: 261901-1–3.