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Ferrogels and magnetoelastomers are composite materials obtained by embeddingmagnetic particles of mesoscopic size in a crosslinked polymeric matrix. Theycombine the reversible elastic deformability of polymeric materials with thehigh responsivity of ferrofluids to external magnetic fields. These materialsstand out, for example, for large magnetostriction as well as significantincrease of the elastic moduli in the presence of external magnetic fields. Bymeans of X-ray micro-computed tomography, position and size of each magneticparticle can be measured with a high degree of accuracy. We here use dataextracted from real magnetoelastic samples as input for coarse-graineddipole-spring modeling and calculations to investigate magnetostriction,stiffening, and changes in the normal modes spectrum. More precisely, we assignto each particle a dipole moment proportional to its volume and set arandomized network of springs between them that mimics the behavior of thepolymeric elastic matrix. Extending our previously developed methods, wecompute the resulting structural changes in the systems, their overalldistortions, as well as the frequency-dependent elastic moduli when magneticinteractions are turned on. Particularly, with increasing magnetization, weobserve the formation of chain-like aggregates, resulting in significantoverall deformations. Interestingly, the static elastic moduli can first show aslight decrease with growing amplitude of the magnetic interactions, before apronounced increase appears upon the chain formation. The change of the dynamicmoduli with increasing magnetization depends on the frequency and can even shownonmonotonic behavior. Overall, we demonstrate how theory and experiments cancomplement each other to learn more about the dynamic behavior of thisinteresting class of materials.

Tunable dynamic moduli of magnetic elastomers: from X-$\mu$CT characterization to mesoscopic modeling