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In the perspective of developing smart hybrid materials with customizedfeatures, ferrogels and magnetorheological elastomers allow a synergy ofelasticity and magnetism. The interplay between elastic and magnetic propertiesgives rise to a unique reversible control of the material behavior by applyingan external magnetic field. Albeit few works have been performed on thetime-dependent properties so far, understanding the dynamic behavior is the keyto model many practical situations, e.g. applications as vibration absorbers.Here we present a way to calculate the frequency-dependent elastic moduli basedon the decomposition of the linear response to an external stress in normalmodes. We use a minimal three-dimensional dipole-spring model to theoreticallydescribe the magnetic and elastic interactions on the mesoscopic level.Specifically, the magnetic particles carry permanent magnetic dipole momentsand are spatially arranged in a prescribed way, before they are linked byelastic springs. An external magnetic field aligns the magnetic moments. On theone hand, we study regular lattice-like particle arrangements to compare withprevious results in the literature. On the other hand, we calculate the dynamicelastic moduli for irregular, more realistic particle distributions. Ourapproach measures the tunability of the linear dynamic response as a functionof the particle arrangement, the system orientation with respect to theexternal magnetic field, as well as the magnitude of the magnetic interactionbetween the particles. The strength of the present approach is that itexplicitly connects the relaxational modes of the system with the rheologicalproperties as well as with the internal rearrangement of the particles in thesample, providing new insight into the dynamics of these remarkable materials.

Dynamic Elastic Moduli in Magnetic Gels: Normal Modes and Linear Response