  A theory of mechanical behaviour of the magneto-sensitive elastomers is
developed in the framework of a linear elasticity approach. Using a regular
rectangular lattice model, different spatial distributions of magnetic
particles within a polymer matrix are considered: isotropic, chain-like and
plane-like. It is shown that interaction between the magnetic particles results
in the contraction of an elastomer along the homogeneous magnetic field. With
increasing magnetic field the shear modulus for the shear deformation
perpendicular to the magnetic field increases for all spatial distributions of
magnetic particles. At the same time, with increasing magnetic field the
Young's modulus for tensile deformation along the magnetic field decreases for
both chain-like and isotropic distributions of magnetic particles and increases
for the plane-like distribution of magnetic particles.
