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Can isotropic Magneto-Active Elastomers (MAEs) undergo giant magnetically induced deformations and exhibit huge magnetorheological effects simultaneously? In this experimental and theoretical study, we reveal how the macroscopic deformation of MAEs relates to the process of particle restructuring caused by application of a magnetic field. For this purpose, MAE cylinders with different aspect ratios and particle loadings are studied in uniform magnetic fields. The axial deformations of the cylinders are acquired using an optical camera. A unified mean-field model proposed in previous studies is adapted to describe the transition of initially isotropic cylinders into transversely isotropic ones. This mechanical transition is caused by the rearrangement of particles into dense columnar structures aligned with the field and is believed to result in a huge magnetorheological effect. Our model however predicts less than three-fold increase in elastic moduli when evaluated along the field direction. This prediction is based on a careful examination of the shear moduli of studied MAEs and the columnar structures. A weak magnetorheological effect explains significant axial deformations measured in the field direction. A strong magnetorheological effect would hinder axial deformations due to an increase in modulus by several orders of magnitude. Not only are the moduli and macroscopic deformations influenced by microstructure evolution, but so is the magnetization of particles, which increases as they rearrange into dense columns. With this study, we show that the unified mean-field model provides quantitative access to hidden material properties such as magnetization and stiffness in MAE samples with different shapes and evolving microstructures.

Composite materials where magnetic micrometer-sized particles are embedded into a compliant polymer matrix are known as magnetorheological or magnetoactive elastomers (MAEs). They are distinguished by huge variations of their physical properties in a magnetic field, which is commonly attributed to the restructuring of the filler. The process of the magnetic-field-induced restructuring in a magnetorheological elastomer is interpreted as progression towards percolation. Such a physical model was previously used to explain the dependence of the magnetic permeability and dielectric permittivity of MAEs on the magnetic field strength. Based on this hypothesis, the magnetorheological effect in MAEs is considered theoretically. The theoretical approach is built upon a self-consistent effective-medium theory for the elastic properties, extended to the variable (field dependent) percolation threshold. The proposed model allows one to describe the large variations (over several orders of magnitude) of the effective elastic moduli of these composite materials, known as the giant magnetorheological (MR) and field-stiffening effects. An existence of a giant magnetic Poisson effect is predicted. The relation of the proposed model to the existing theories of the MR effect in MAEs is discussed. The results can be useful for applications of MAEs in magnetic-field controlled vibration dampers and isolators., Comment: 19 pages, 6 figures, divided into sections, new figures and information added, article name and abstract modified

We propose a theoretical approach for calculating effective electric and magnetic properties of composites with field-dependent restructuring of the filler. The theory combines the Bruggeman-Landauer approximation extended to a field-dependent (variable) percolation threshold with the approximate treatment of nonlinearity of material properties. Theoretical results are compared with experiments on magnetorheological elastomers, which in the context of investigated phenomena are often called magnetoactive elastomers (MAEs). In MAEs with soft polymer matrices, the mutual arrangement of inclusions changes in an applied magnetic field. This reorganization of the microstructure leads to unconventionally large changes of electrical and magnetic properties. Obtained theoretical results describe observed phenomena in MAEs well. Qualitative agreement between theory and experiment is demonstrated for the magnetodielectric effect. In the case of magnetic permeability, quantitative agreement is achieved. The theoretical approach presented can be useful for development of field-controlled smart materials and design of smart structures on their basis, because the field dependence of physical properties can be predicted.

It is shown that in external magnetic fields, a uniaxial magnetic anisotropy comes into being in a magnetoactive elastomer (MAE). The magnitude of the induced uniaxial anisotropy grows with the increasing external magnetic field. The filler particles are immobilized in the matrix if the MAE sample is cooled below 220 K, where the anisotropy can be read out. The cooling of the sample is considered as an alternative methodological approach to the experimental investigation of the magnetized state of MAEs. The appearance of magnetic anisotropy in MAE is associated with restructuring of the filler during magnetization, which leads to an additional effective field felt by the magnetization. It is found that the magnitude of the effective magnetic anisotropy constant of the MAE is approximately two times larger than its effective shear modulus in the absence of magnetic field. It is proposed that the experimentally observed large (about 40) ratio of the magnetic anisotropy constant of the filler to the shear modulus of the matrix deserves attention for the explanation of magnetic and magnetoelastic properties of MAEs. It may lead to additional rigidity of the elastic subsystem increasing the shear modulus of the composite material through the magnetomechanical coupling., Comment: 20 pages, 7 figures

Magnetic properties of a magnetoactive elastomer (MAE) filled with {\mu}m-sized soft-magnetic iron particles have been experimentally studied in the temperature range between 150 K and 310 K. By changing the temperature, the elastic modulus of the elastomer matrix was modified and it was possible to obtain magnetization curves for an invariable arrangement of particles in the sample as well as in the case when the particles were able to change their position within the MAE under the influence of magnetic forces. At low (less than 220 K) temperatures, when the matrix becomes rigid, the magnetization of the MAE does not show a hysteresis behavior and it is characterized by a negative value of the Rayleigh constant. At room temperature, when the polymer matrix is compliant, a magnetic hysteresis exists and exhibits local maxima of the field dependence of the differential magnetic susceptibility. The appearance of these maxima is explained by the elastic resistance of the matrix to the displacement of particles under the action of magnetic forces., Comment: 16 pages, 6 figures

The influence of an external magnetic field on the static shear strain and the effective shear modulus of a magnetoactive elastomer (MAE) is studied theoretically in the framework of a recently introduced approach to the single-particle magnetostriction mechanism [V. M. Kalita et al, Phys. Rev. E 93, 062503 (2016)]. The planar problem of magnetostriction in an MAE with soft magnetic inclusions in the form of a thin disk (platelet) having the magnetic anisotropy in the plane of this disk is solved analytically. An external magnetic field acts with torques on magnetic filler particles, creates mechanical stresses in the vicinity of inclusions, induces shear strain and increases the effective shear modulus of these composite materials. It is shown that the largest effect of the magnetic field on the effective shear modulus should be expected in MAEs with soft elastomer matrices, where the shear modulus of the matrix is less than the magnetic anisotropy constant of inclusions. It is derived that the effective shear modulus is non-linearly dependent on the external magnetic field and approaches the saturation value in magnetic fields exceeding the field of particle anisotropy. It is shown that model calculations of the effective shear modulus correspond to a phenomenological definition of effective elastic moduli and magnetoelastic coupling constants. Obtained theoretical results compare well with known experimental data. Determination of effective elastic coefficients in MAEs and their dependence on magnetic field is discussed. The concentration dependence of the effective shear modulus at higher filler concentrations has been estimated using the method of Pad\'e approximants, which correctly predicts that both the absolute and relative changes of the magnetic-field dependent effective shear modulus will significantly increase with the growing concentration of filler particles., Comment: 29 pages, 9 figures