Remanent magnetic response of hard magnetorheological elastomer foams: Fabrication, microstructure characterization and modeling

This work deals with the experimental, numerical and theoretical study of the purely magnetic response of hard magnetorheological elastomer ($h$-MRE) foams of variable particle and porosity content. First, the fabrication and experimental measurement of the remanent magnetic flux of the $h$-MRE foams are presented. We find that at lower particle content, the foam comprises closed-cell porosity, with the voids having a variable size and ellipsoidal shape. As the particle content in the matrix increases, the voids become smaller in size and more spherical in shape, while the porosity decreases. We show experimentally that the remanent magnetic flux is entirely independent of the shape and orientation of the voids. Image-based morphological analysis of the $h$-MRE foam microstructure subsequently allows to reconstruct numerically unit-cells that share the same statistics as those of the experimental foams. These unit-cells are used to construct an explicit theoretical model with magnetic dissipation. We show that the remanent magnetization is a linear function of the overall particle volume fraction in the foam. The model is further used to scale up the analysis and solve the experimental boundary value problem of a permanently magnetized $h$-MRE cube, and the numerical estimates show excellent agreement with the experiments. Finally, the numerical model is shown to match available analytical solutions for the remanent magnetic flux of parallelepiped magnets.