Magnetoelasticity of gels

Magnetoelastic gel is an active material that is used widely these days. The behavior of these multifunctional gels is derived from a polymer matrix and magnetoresponsive inclusions. The polymer matrix provides structural integrity as well as load bearing capacity to the magnetoelastic gel. The magnetic behavior of the magnetoelastic gel is attributed to a large number of nano-to-micron-sized magnetic particles disbursed in the polymer matrix. The magnetoelastic gel is said to be diluted if the interparticle interactions are negligible/small or concentrated if there are strong interparticle interactions. We consider strong interparticle interactions in the magnetoelastic gel. When the magnetic field is applied to the magnetoelastic gel, the disbursed magnetic particles tend to translate and rotate to a new deformed configuration. Due to these translations and rotations of the many magnetoelastic particles, the polymer matrix around each particle deforms. These micro-deformations then coalesce and lead to the overall macroscopic deformation of the magnetoelastic gel. Both magnetization and mechanical strain characterize the magnetoelastic behavior of the magnetoelastic gel. In this article, an energy minimization approach is followed to find the equilibrium magnetization and strain. We formulate the total energy of the magnetoelastic gel on multiple-length scales and minimize it to obtain these equilibrium magnetization and mechanical strain. We also investigate the effect of particle size and polarization under the framework of energy minimization.