  Ferrogels are smart soft materials, consisting of a polymeric network and
embedded magnetic particles. Novel phenomena, such as the variation of the
overall mechanical properties by external magnetic fields, emerge consequently.
However, the dynamic behavior of ferrogels remains largely unveiled. In this
paper, we consider a one-dimensional chain consisting of magnetic dipoles and
elastic springs between them as a simple model for ferrogels. The model is
evaluated by corresponding simulations. To probe the dynamics theoretically, we
investigate a continuum limit of the energy governing the system and the
corresponding equation of motion. We provide general classification scenarios
for the dynamics, elucidating the touching/detachment dynamics of the magnetic
particles along the chain. In particular, it is verified in certain cases that
the long-time relaxation corresponds to solutions of shock-wave propagation,
while formations of particle pairs underlie the initial stage of the dynamics.
We expect that these results will provide insight into the understanding of the
dynamics of more realistic models with randomness in parameters and
time-dependent magnetic fields.
