A fractional calculus approach to modeling rheological behavior of soft magnetic elastomers

•A fractional rheological model for magnetorheological elastomers is proposed.•Model parameters' dependence on magnetic field is considered.•A connection between constitutive fractional derivative order and material structure is established.

A fractional calculus approach is applied to model constitutive behavior of magnetorheological elastomers. To test the model results magnetorheological elastomers containing different concentrations of iron particles have been synthesized and their rheological behavior in various magnetic fields has been studied experimentally. The fractional model parameters were found from fitting the experimental data. An excellent agreement between experimental results and the model predictions has been obtained. Correlation between the values of the order of the constitutive equation and structuring of magnetic filler governed by the balance between elastic and magnetic interactions has been formulated. It has been shown that the fractional rheological model can satisfactorily describe dynamic behavior of magnetorheological elastomers in magnetic field.

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