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Magneto-sensitive elastomers in a homogeneous magnetic field: a regular rectangular lattice model

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.