  We introduce and investigate a coarse-grained model for quasi one-dimensional
ferrogels. In our description the magnetic particles are represented by hard
spheres with a magnetic dipole moment in their centers. Harmonic springs
connecting these spheres mimic the presence of a cross-linked polymer matrix. A
special emphasis is put on the coupling of the dipolar orientations to the
elastic deformations of the matrix, where a memory effect of the orientations
is included. Although the particles are displaced along one spatial direction
only, the system already shows rich behavior: as a function of the magnetic
dipole moment, we find a phase transition between "soft-elastic" states with
finite interparticle separation and finite compressive elastic modulus on the
one hand, and "hardened" states with touching particles and therefore diverging
compressive elastic modulus on the other hand. Corresponding phase diagrams are
derived neglecting thermal fluctuations of the magnetic particles. In addition,
we consider a situation in which a spatially homogeneous magnetization is
initially imprinted into the material. Depending on the strength of the
magneto-mechanical coupling between the dipole orientations and the elastic
deformations, the system then relaxes to a uniaxially ferromagnetic, an
antiferromagnetic, or a spiral state of magnetization to minimize its energy.
One purpose of our work is to provide a largely analytically solvable approach
that can provide a benchmark to test future descriptions of higher complexity.
From an applied point of view, our results could be exploited, for example, for
the construction of novel damping devices of tunable shock absorbance.
