Theoretical models for magneto-sensitive elastomers: A comparison between continuum and dipole approaches
D. Romeis, P. Metsch, M. Kaestner, M. Saphiannikova,
Volume: Accepted for publication.
Published: 2017
Abstract
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 in how far the dipolar mean field approach is superior to other
dipole models.