  Soft elastic composite materials containing particulate rigid inclusions in a
soft elastic matrix are candidates for developing soft actuators or tunable
damping devices. The possibility to reversibly drive the rigid inclusions
within such a composite together to a close-to-touching state by an external
stimulus would offer important benefits. Then, a significant tuning of the
mechanical properties could be achieved due to the resulting mechanical
hardening. For a long time, it has been argued whether a virtual touching of
the embedded magnetic particles with subsequent detachment can actually be
observed in real materials, and if so, whether the process is reversible. Here,
we present experimental results that demonstrate this phenomenon in reality.
Our system consists of two paramagnetic nickel particles embedded at finite
initial distance in a soft elastic polymeric gel matrix. Magnetization in an
external magnetic field tunes the magnetic attraction between the particles and
drives the process. We quantify the scenario by different theoretical tools,
i.e., explicit analytical calculations in the framework of linear elasticity
theory, a projection onto simplified dipole-spring models, as well as detailed
finite-element simulations. From these different approaches, we conclude that
in our case the cycle of virtual touching and detachment shows hysteretic
behavior due to the mutual magnetization between the paramagnetic particles.
Our results are important for the design and construction of reversibly tunable
mechanical damping devices. Moreover, our projection on dipole-spring models
allows the formal connection of our description to various related systems,
e.g., magnetosome filaments in magnetotactic bacteria.
