  In this contribution a magnetoactive elastomer (MAE) of mixed content, i.e.,
a polymer matrix filled with a mixture of magnetically soft and magnetically
hard spherical particles, is considered. The object we focus at is an
elementary unit of this composite, for which we take a set consisting of a
permanent spherical micromagnet surrounded by an elastomer layer filled with
magnetically soft microparticles. We present a comparative treatment of this
unit from two essentially different viewpoints. The first one is a
coarse-grained molecular dynamics simulation model, which presents the
composite as a bead-spring assembly and is able to deliver information of all
the microstructural changes of the assembly. The second approach is entirely
based on the continuum magnetomechanical description of the system, whose
direct yield is the macroscopic field-induced response of the MAE to external
field, as this model ignores all the microstructural details of the
magnetization process. We find that, differing in certain details, both
frameworks are coherent in predicting that a unit comprising magnetically soft
and hard particles may display a non-trivial re-entrant
(prolate/oblate/prolate) axial deformation under variation of the applied field
strength.
  The flexibility of the proposed combination of the two complementary
frameworks enables us to look deeper into the manifestation of the magnetic
response: with respect to the magnetically soft particles, we compare the
linear regime of magnetization to that with saturation, which we describe by
the Fr\"{o}hlich-Kennelly approximation; with respect to the polymer matrix, we
analyze the dependence of the re-rentrant deformation on its rigidity.
