  Colloidal magnetic particles embedded in an elastic polymer matrix constitute
a smart material called ferrogel. It responds to an applied external magnetic
field by changes in elastic properties, which can be exploited for various
applications like dampers, vibration absorbers, or actuators. Under appropriate
conditions, the stress-strain behavior of a ferrogel can display a fascinating
feature: superelasticity, the capability to reversibly deform by a huge amount
while barely altering the applied load. In a previous work, using numerical
simulations, we investigated this behavior assuming that the magnetic moments
carried by the embedded particles can freely reorient to minimize their
magnetic interaction energy. Here, we extend the analysis to ferrogels where
restoring torques by the surrounding matrix hinder rotations towards a
magnetically favored configuration. For example, the particles can be
chemically cross-linked into the polymer matrix and the magnetic moments can be
fixed to the particle axes. We demonstrate that these systems still feature a
superelastic regime. As before, the nonlinear stress-strain behavior can be
reversibly tailored during operation by external magnetic fields. Yet, the
different coupling of the magnetic moments causes different types of response
to external stimuli. For instance, an external magnetic field applied parallel
to the stretching axis hardly affects the superelastic regime but stiffens the
system beyond it. Other smart materials featuring superelasticity, e.g.
metallic shape-memory alloys, have already found widespread applications. Our
soft polymer systems offer many additional advantages like a typically higher
deformability and enhanced biocompatibility combined with high tunability.
