Incorporating magnetizable microparticles into an elastic polymer matrix results in an interesting composite material with a strong magneto-mechanical coupling, when the sample is exposed to a magnetic field. This coupling causes a deformation and noticeable changes in the mechanical moduli. The sign and strength of the material response crucially depends on the actual distribution of the magnetizable particles and whether or not these particles can additionally rearrange with respect to the surrounding polymer network. Based on a dipole approximation for the magnetic interactions we develop a mean-field approach for smeared distributions of particles inside an ellipsoidal sample. In accordance with experimental observations  we consider the formation of elongated microstructures in direction of the applied magnetic field. It turns out that in the thermodynamic limit of macroscopically large samples the case of elongated structure formation can be solved very efficiently. Therefore, we are able to systematically study the behavior of magneto-sensitive elastomers for a great range of parameters, such as the thickness and density of such microstructures or the initial shape factor of the sample. As pointed out in previous work  we can furthermore identify an interplay between a shape effect and an effect due to the microstructure relevant for the description of magneto-sensitive elastomers. Our model allows a detailed characterization of this interplay, e. g. the construction of a phase diagram, and the resulting behavior of the sample. The results of our mean-field model are compared with the predictions of a microscopic continuum model of similar composites proving our approach to work rather well.
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