  Ferrogels and magnetoelastomers are composite materials obtained by embedding
magnetic particles of mesoscopic size in a crosslinked polymeric matrix. They
combine the reversible elastic deformability of polymeric materials with the
high responsivity of ferrofluids to external magnetic fields. These materials
stand out, for example, for large magnetostriction as well as significant
increase of the elastic moduli in the presence of external magnetic fields. By
means of X-ray micro-computed tomography, position and size of each magnetic
particle can be measured with a high degree of accuracy. We here use data
extracted from real magnetoelastic samples as input for coarse-grained
dipole-spring modeling and calculations to investigate magnetostriction,
stiffening, and changes in the normal modes spectrum. More precisely, we assign
to each particle a dipole moment proportional to its volume and set a
randomized network of springs between them that mimics the behavior of the
polymeric elastic matrix. Extending our previously developed methods, we
compute the resulting structural changes in the systems, their overall
distortions, as well as the frequency-dependent elastic moduli when magnetic
interactions are turned on. Particularly, with increasing magnetization, we
observe the formation of chain-like aggregates, resulting in significant
overall deformations. Interestingly, the static elastic moduli can first show a
slight decrease with growing amplitude of the magnetic interactions, before a
pronounced increase appears upon the chain formation. The change of the dynamic
moduli with increasing magnetization depends on the frequency and can even show
nonmonotonic behavior. Overall, we demonstrate how theory and experiments can
complement each other to learn more about the dynamic behavior of this
interesting class of materials.
