Magnetorheological elastomer (MRE)-based semi-active vibration mitigation device demands a mathematical representation of its smart characteristics. To model the material behavior over broadband frequency, the simplicity of the mathematical formulation is very important. Material modeling of MRE involves the theory of viscoelasticity, which describes the properties intermediate between the solid and the liquid. In the present study, viscoelastic property of MRE is modeled by an integer and fractional order derivative approaches. Integer order-based model comprises of six parameters, and the fraction order model is represented by five parameters. The parameters of the model are identified by minimizing the error between the response from the model and the dynamic compression test data. Performance of the model is evaluated with respect to the optimized parameters estimated at different sets of regularly spaced arbitrary input frequencies. A linear and quadratic interpolation function is chosen to generalize the variation of parameters with respect to the magnetic field and frequency. The predicted response from the model revealed that the fractional order model describes the properties of MRE in a simplest form with reduced number of parameters. This model has a greater control over the real and imaginary part of the complex stiffness, which facilitates in choosing a better interpolating function to improve the accuracy. Furthermore, it is confirmed that the realistic assessment on the performance of a model is based on its ability to reproduce the results obtained from optimized parameters.

Accurate modeling of material behavior is very critical for the success of magnetorheological elastomer-based semi-active control device. The material property of magnetorheological elastomer is sensitive to the frequency, magnetic field and the input strain. Additionally, these properties are unique for a particular combination of matrix and the filler loading. An experimental-based characterization approach is costly and time consuming as it demands a large amount of experimental data. This process can be simplified by adopting material modeling approach. The material modeling of magnetorheological elastomer is an extension of conventional viscoelastic constitutive relations coupled with hysteresis and magnetic field sensitive attributes. In the present study, a mathematical relation to represent the frequency, magnetic field and strain dependent behavior of magnetorheological elastomer is presented. The viscoelastic behavior is represented by a fractional zener element and the magnetic field and strain dependent attributes incorporated in the model by a magnetic spring and linearized Bouc-–Wen element, respectively. The proposed model comprised of a total of eight parameters, which are identified by minimizing the least square error between the model predicted and the experimental response. The variations of each parameter with respect to the operating conditions are represented by a generalized expression. The parameters estimated from the generalized expression are used to assess the ability of the model in describing the dynamic response of magnetorheological elastomer. The proposed model effectively predicted the stiffness characteristics with an accuracy, more than 94.3% and the corresponding accuracy in predicting the damping properties is above 90.1%. This model is capable of fitting the experimental value with a fitness value of more than 93.22%.

The rheological properties of magnetorheological elastomers are influenced by magnetically sensitive fillers and the elastomer matrix. The ability to respond to an external magnetic field is imparted by the fillers, while the load-bearing capability is determined by the matrix type. In this paper, the effect of matrix material on the properties of magnetorhological elastomer is explored experimentally. Carbonyl iron particle content is varied by 0%, 15% and 25% by volume to produce magnetorheological elastomer samples using natural rubber, silicone rubber and nitrile butadiene rubber matrices. Forced transmissibility test approach was employed to evaluate the field induced variations in the dynamic stiffness and loss factor of magnetorheological elastomers. The dynamic stiffness of nitrile butadiene rubber is the highest, while that of silicone rubber is the lowest. Addition of carbonyl iron particles significantly improves stiffness, although these gains depend on the properties of unfilled matrix. The addition of 25% by volume of carbonyl iron particle increased the dynamic stiffness of a silicone rubber matrix based magnetorheological elastomer by 67.78%, while the similar change in magnetorheological elastomer with nitrile butadiene rubber matrix was 38.58%. The field dependent response of magnetorheological elastomers is governed by the matrix and ferromagnetic filler concentration. These qualities are higher in magnetorheological elastomer with a low initial dynamic stiffness matrix and lower in magnetorheological elastomers with a stiffer matrix.