The dynamic modulus and the loss factor of magnetorheological elastomers (MREs) of various compositions and anisotropies are studied by dynamic torsion oscillations performed in the absence and in the presence of an external magnetic field. The emphasis is on the Payne effect, i.e. the dependence of the elastomer magnetorheological characteristics on the strain amplitude and their evolution with cyclically increasing and decreasing strain amplitudes. MREs are based on two silicone matrices differing in storage modulus (soft, G′ ∼ 10³ Pa, and hard, G′ ∼ 10⁴ Pa, matrices). For each matrix, the concentration of carbonyl iron particles with diameters of 3–5 μm was equal to 70 and 82 mass% (22 and 35 vol%, respectively) in the composite material. Samples for each filler content, isotropic and aligned-particles, are investigated. It is found that the Payne effect significantly increases in the presence of an external magnetic field and varies with the cyclical loading which reaches saturation after several cycles. The results are interpreted as the processes of formation–destruction–reformation of the internal filler structure under the simultaneously applied mechanical force and magnetic field. Impacts of matrix elasticity and magnetic interactions on the filler alignment are elucidated.

An equivalent circuit, consisting of bulk and distributed elements, is derived for describing the properties of a potential metamaterial element capable of providing negative effective permeability. It is the singly split double ring (SSDR), a special case of the split ring resonator (J. B. Pendry et al., IEEE Trans. Microwave Theory Tech. 47, 2075 (1999)), obtained when the gap capacitance in the inner ring is infinitely large. The variables are the inter-ring voltage and the currents flowing in the inner and outer rings. The excitation is assumed in the form of a spatially constant temporally varying magnetic field. The functions, showing the angular variation of the variables, are found by solving a set of differential equations with boundary conditions imposed at the position of the split. It is shown from the analytical solution that the SSDR can have resonant frequencies in the full spectrum from very low to very high frequencies. It is pointed out in particular that whenever the mean diameter of the ring is equal to an odd multiple of the half wavelength it is always possible to find a set of parameters which will give rise to resonance. As examples the resonant frequencies are determined for eight sets of parameters. Results are also derived by replacing the distributed circuit with a number of discrete circuits. It is finally shown that the results obtained from the equivalent circuit model are in excellent agreement with those derived from the MICRO-STRIPES numerical package which solves Maxwell’s equations in the time domain.

A theoretical and experimental study of magnetic metamaterials with unit cells containing two resonant elements is presented. The properties of these structures, consisting of split rings, are governed by strongly anisotropic magnetic coupling between individual elements. This coupling leads to propagation of slow magnetoinductive waves in the vicinity of the resonant frequency. The wavelength of magnetoinductive waves is much smaller than the free-space wavelength of the electromagnetic radiation. This opens up the possibility of manipulating the near field on a subwavelength scale. We develop a theoretical formulation for coupled chains of metamaterial elements allowing the tailoring of their guiding properties in the near field. In a comprehensive analysis modes of coupled waveguides supporting forward and/or backward waves are identified and the corresponding hybridization mechanisms for dispersion equations of magnetoinductive waves are determined. Analytical predictions are verified both experimentally and numerically on a variety of coupled waveguides. The approach can be employed for the design of near-field manipulating devices.