To the theory of shear elastic properties of magnetic gels

We present results of theoretical study of elastic shear modulus of magnetic gels, consisting of single non Brownian magnetic particles, homogeneously (gas-like) distributed in an elastic matrix. The composite is placed in magnetic field, perpendicular to the direction of the sample shear. Effect of both, magnetically hard and soft particles is studied. In order to get mathematically rigorous results, we have restricted ourselves by the analysis of the composites with low concentration of the particles and neglected any interactions between them. Only small deformations of the system were considered. Analysis shows that effect of magnetic field on the macroscopic (measurable) shear modulus of the composite can be comparable with that, provided by the presence of the rigid inclusions in the elastic matrix. The suggested asymptotic model can be a robust background for the study of the systems with moderate or high concentration of the particles.