Magnetoelastic modelling of elastomers

In this paper we first summarize the equations governing the deformation of magneto-sensitive (MS) elastic solids with particular reference to elastomers whose mechanical properties may be changed rapidly by the application of a magnetic field. These ‘smart materials’ typically consist of micron-sized ferrous particles dispersed within an elastomeric matrix. Constitutive relations for isotropic MS-elastic solids are examined. The equations are then applied to a representative geometry appropriate for applications, that in which the material is confined to a circular cylindrical tube in the presence of a radial magnetic field. The material is then subject to an axial shear deformation. Results are illustrated for two specific material models, for each of which the shear stiffness of the material increases with the magnetic field strength, as observed in experiments on MS elastomers.