ИСТИНА

Magnetoactive elastomers (or MAEs) are composite polymer materials consisting of relatively soft polymeric matrix and ferromagnetic filler particles of different sizes. Such microstructure allows to control various properties of MAEs, for example their shape and stiffness. Due to their high responsiveness to external field-based stimuli, the applications include tuneable mechanical devices as well as cases where elastic subsystem interaction with an external field is important. MAEs exhibit a vast array of interesting physical effects: magnetostriction, magnetorheological effect, magnetically enhanced Payne effect, magnetic and mechanical hysteresis, memory effects etc. This work aims to propose, analyze and compare several fractional rheological models of MAEs. Rheological circuits are phenomenological models used to describe dynamic behavior of a viscoelastic material. We utilize them to model field-dependent viscoelasticity of MAEs. To make rheological circuits more flexible while keeping the simplicity of their forms we make use of fractional calculus and introduce elements with fractional differential stress-strain relations into classical rheological models. In order to obtain data for analysis MAE samples with several different values of carbonyl iron filler concentration have been synthesized. Theoretical model parameters have been calculated via fitting experimental frequency dependences of MAE’s dynamic moduli measured under dynamic torsion oscillations in linear viscoelastic regime. It was shown that the simplest fractional rheological models with one fractional element can be used to adequately describe MAE response at weak and for some cases strong magnetic fields where the main contribution to the MAEs mechanical properties comes either from polymer network in the low-field case or ferromagnetic particle aggregates in the high-field case. However, for medium magnetic fields with the expected significant restructuring of the magnetic filler more complex models are needed as using simple circuits (like the Zener model) leads to large errors and inconsistencies in fitting the experimental data. According to the findings presented in this work, two-fractional-element models provide highly accurate results for a wide range of magnetic fields. The main focus of this particular research was the fractional generalized Maxwell (or Maxwell-Wiechert) model with two branches. High effectiveness of this model in describing mechanical response of MAEs for a wide range of external magnetic field values was demonstrated. Possible interpretation of two fractional branches and their fractional order parameters in generalized Maxwell model as representations of MAE components (namely, polymer network and ferromagnetic filler) was proposed. Financial support of the Russian Science Foundation (project 16-15-00208) is acknowledged.