Modelling of magneto-sensitive elastomers

Magneto-sensitive (MS) elastomers are a class of smart materials that instantly change their mechanical behavior in response to the application of a magnetic field. These materials are in general a mixture of micron-sized ferrous particles dispersed in an elastomer. In this paper we first summarize the full system of equations for deformable MS solids in an electro-magnetic field. Constitutive relations for an isotropic Cauchy-elastic solid are derived by making simplifying assumptions on the electromagnetic characteristics of the MS elastomer. To illustrate the utility of these models, we consider the shear deformation of a MS elastomer between two parallel plates under the application of a magnetic field normal to the plates.