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One of the central appealing properties of magnetic gels and elastomers isthat their elastic moduli can reversibly be adjusted from outside by applyingmagnetic fields. The impact of the internal magnetic particle distribution onthis effect has been outlined and analyzed theoretically. In most cases,however, affine sample deformations are studied and often regular particlearrangements are considered. Here we challenge these two major simplificationsby a systematic approach using a minimal dipole-spring model. Starting fromdifferent regular lattices, we take into account increasingly randomizedstructures, until we finally investigate an irregular texture taken from a realexperimental sample. On the one hand, we find that the elastic tunabilityqualitatively depends on the structural properties, here in two spatialdimensions. On the other hand, we demonstrate that the assumption of affinedeformations leads to increasingly erroneous results the more realistic theparticle distribution becomes. Understanding the consequences of theassumptions made in the modeling process is important on our way to support animproved design of these fascinating materials.

Structural control of elastic moduli in ferrogels and the importance of non-affine deformations