The results of a study of magnetoactive elastomers (MAEs) consisting of an elastomer matrix with embedded ferromagnetic particles are presented. A continuous critical bending induced by the magnetic field, characterized by a critical exponent for the bending magnitude, and the derivative of which has a singularity in the critical region is reported for the first time. The mechanical stability loss and the symmetry reduction of the magnetic state, which are interrelated with each other, take place at the critical point. The magnetization in the high-symmetric state (below the critical point) is directed along the magnetic field and the torque is absent. Above the critical point, the magnetization and the magnetic field are noncollinear and there arises a torque, which is self-consistent with the bending. The magnetic field dependence of the MAE bending was found to have a hysteresis, which is associated with the magneto-rheological effect. The shape memory effect was also obtained for the MAE bending in a cycle consisting of magnetization, cooling (at H ≠ 0), and heating (at H = 0). The influence of the critical glass transition temperature of the matrix, as well as its melting/solidification temperature, on the magnetic shape memory effect was studied.

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The effect of anomalous bending in a system of magnetically soft ferromagnetic stripes located on a highly elastic plate of elastomer has been studied both experimentally and theoretically. It was found that the magnetic-field dependences for the bending of plates with ferromagnetic stripes have a critical character with a reproduced hysteresis emerging in the repeated cycles of the magnetic field increasing and decreasing. It was found that the magnetically induced bending has a large magnitude, so that the magnetic moments of the stripes at the bending can be directed almost perpendicularly to the magnetic field. In a strong magnetic field, the effect of stripe orientation is observed, which occurs due to the orienting action of Zeeman interaction. It was shown that the hysteresis phenomenon observed at the bending of a plate with stripes is associated with a strong nonlinearity of magnetostatic interaction between the stripes at their magnetization. The hysteresis recurrence is caused by elastic forces arising at the elastomer bending and competing with magnetostatic dipole-dipole interactions between the stripes. The critical points of transitions between the 'discrete lattice' state of stripes and the state of laterally touching stripes were determined. A model of the phenomenon concerned was proposed which is in good agreement with experimental data.

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The features of the critical bending deformation and magnetization of a magnetoactive elastomer (MAE) beam with a fixed end in a transverse uniform magnetic field have been studied. After the beam reaches a critical bending, the symmetry of the beam shape and the symmetry of the MAE magnetic state change spontaneously. At the critical point, a continuous transition from the highly symmetric magnetic state in the unbent MAE beam to the low symmetric magnetic state in the bent MAE beam (this is the angular state with the effective magnetization inclined to the field) takes place. The beam bending occurs due to the gain in the magnetic energy of the beam. The formation of an angular magnetic state in it has a magnetoelastic origin and is characterized by the critical behavior of the mutually related bending and longitudinal effective magnetization of the MAE, but it is the magnetization that plays the role of order parameter. Furthermore, there is no longitudinal magnetization in the absence of bending and, vice versa, there is no bending in the absence of longitudinal magnetization. The influence of a low remanent magnetization, which eliminates the uncertainty in the bending direction, on the critical bending has been analyzed. The role of the magnetorheological effect, which affects the critical field magnitude and leads to the appearance of field-induced bending hysteresis near the critical point, has also been elucidated.