Shear modulus of isotropic ferrogels

•Magnetic field enhances shear modulus of magnetic gels.•The shear modulus non monotonic depends on the field.•The magnetorheological effects are more pronounced in soft gels than in rigid elastomers. We present results of theoretical study of magnetorheological effect in ferrogels with magnetizable spherical particles chaotically distributed in a current gel. To avoid intuitive constructions with uncontrolled accuracy and adequacy, the analysis is done in the frames of the mathematically regular pair approximation. Our results demonstrate non monotonic increase of the composite shear modulus with the applied magnetic field. This effect is stronger for the systems with the soft gel, than for the relatively rigid ones.