  One of the central appealing properties of magnetic gels and elastomers is
that their elastic moduli can reversibly be adjusted from outside by applying
magnetic fields. The impact of the internal magnetic particle distribution on
this effect has been outlined and analyzed theoretically. In most cases,
however, affine sample deformations are studied and often regular particle
arrangements are considered. Here we challenge these two major simplifications
by a systematic approach using a minimal dipole-spring model. Starting from
different regular lattices, we take into account increasingly randomized
structures, until we finally investigate an irregular texture taken from a real
experimental sample. On the one hand, we find that the elastic tunability
qualitatively depends on the structural properties, here in two spatial
dimensions. On the other hand, we demonstrate that the assumption of affine
deformations leads to increasingly erroneous results the more realistic the
particle distribution becomes. Understanding the consequences of the
assumptions made in the modeling process is important on our way to support an
improved design of these fascinating materials.
