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Magnetorheological elastomers (MRE), or magnetoactive elastomers, have been studied by researchers for a long time. MRE represents the soft polymer medium with embedded ferro- (ferri-) magnetic micro- (nano-) particles. Attractive mechanical properties of the composites and their tunability with magnetic field were of prior interest for investigations and practical implementation. Magnetorheological effect, magnetodeformational effect, high bending properties, immediate response and remote control allows to use of MRE in a wide range of applications from engineering sensors and valves up to biomedical devices. Recent advances in MRE and composites based on it show interesting peculiarities of electrical and magnetic properties. The possibility to control magnetic properties of MRE by varying concentration of particles became the direction of investigation for 3D-printing and tunable magnetization gradient. Their mechanical response to magnetic field can be also set by the shape of the particular element (pillars array, zig-zag structures, tubes, etc.) The multifunctional actuators based on such MRE elements were demonstrated [1]. Moreover, since the possible compositions of MRE vary in a wide range, their biocompatibility is easily achievable, making them promising for biomedical applications. One of the examples of biomedical implementation of MRE is the seal for complex retinal detachment treatment [2,3]. Biocompatible element with excellent mechanical bending properties and magnetic susceptibility can be effectively held by a silicon-covered buckle of permanent magnets allowing good retina fixation. Mechanical properties of the composite can be utilized for energy harvesting application. This can be achieved in layered composite based on MRE and piezopolymer substrate [4]. Due to gradient magnetic field bending deformation of the structure occurs which can be tuned by the rate of magnetic field switching and the value of magnetic field. The resonance of oscillations was also received in the AC magnetic field. Tunable energy utilization by novel composites allows to develop different types of sensors, energy harvesting devices and devices for mechanotronics. Magnetodielectric effect (MDE) in MRE was studied experimentally and numerically and it revealed the increase of effective permittivity under an external magnetic field [5,6]. The mechanism of MDE is associated with the displacement of microparticles in soft elastic medium. The movement of particles in polymers with relatively low values of Young’s modulus can be essential under applied external fields. Rearrangement of conductive filler changes the effective capacitance of the MRE filled capacitor. Thus, each FM particle induces and, at the same time, is affected by an elastic force. Particles displacement also allows the elastic coupling between different fillers, if several types of particles are used in the material. Any shift of the particles inside the polymer matrix produces internal stresses affecting the distribution and interactions of another filler type. Magnetoelectric effect was observed in three component MAE based on silicone matrix with a mixture of ferromagnetic and ferroelectric microparticles [7]. The stresses induced by ferromagnetic particles shifting under applied external magnetic fields affect the state of the second type of particles – ferroelectric, changing the polarization state of the material. Shifting of ferroelectric particles under electric field cause the inverse magnetodeformational effect through elastic interactions. Thus, such materials can be considered as composite multiferroics. The contribution of elastic interaction between particles of different types was investigated numerically [8]. The suggested results can be used for the optimization of structural properties of composite materials to achieve higher efficiency in magnetoelectrical transformation. This means that such materials can be used in various fields: ranging from biomedical, where the mutual influence of particle movements under applied external magnetic or electric fields as well as mechanical deformations of the matrix are required; to engineering for electromagnetic energy harvesting.