Theoretical models for magneto-sensitive elastomers: A comparison between continuum and dipole approaches

In the literature, different theoretical models have been proposed to describe the properties of systems which consist of magnetizable particles that are embedded into an elastomer matrix. It is well known that such magneto-sensitive elastomers display a strong magneto-mechanical coupling when subjected to an external magnetic field. Nevertheless, the predictions of available models often vary significantly since they are based on different assumptions and approximations. Up to now the actual accuracy and the limits of applicability are widely unknown. In the present work, we compare the results of a microscale continuum and a dipolar mean field approach with regard to their predictions for the magnetostrictive response of magneto-sensitive elastomers and reveal some fundamental relations between the relevant quantities in both theories. It turns out that there is a very good agreement between both modeling strategies, especially for entirely random microstructures. In contrast, a comparison of the finite-element results with a modified approach, which-similar to the continuum model-is based on calculations with discrete particle distributions, reveals clear deviations. Our systematic analysis of the differences shows to what extent the dipolar mean field approach is superior to other dipole models.