Modeling and finite element simulation of the magneto-mechanical behavior of ferrogels

In our previous study (see Ref. Attaran et al. (in press) [1]) we formulated a continuum model for ferrogels considering them as multicomponent materials. In the present work a reduced model for ferrogels is presented consisting only of a polymer network (P) and fixed magnetic particles (f). The reduced model is solved using the finite element method where the only degrees of freedom are mechanical displacement and magnetic potential. Elongation and contraction of a ferrogel are observed parallel and perpendicular to the applied magnetic field direction, respectively. These results are in a good qualitative agreement with experimental results. With our modeling approach, we were able to investigate (i) the influence of the magnetic field on the polymer gel containing magnetic particles and (ii) the resulting mechanical deformation of a ferrogel. •A reduced continuum model for ferrogels, consisting of a polymer network and fixed magnetic particles, is presented.•A coupled magneto-mechanical problem is formulated and solved numerically using the Finite Element Method in 2D.•Deformation of a ferrogel in a magnetic field for a circular gel and a strip of a ferrogel is investigated.•Elongation of the ferrogel is observed in the direction of the applied magnetic field.•Contraction of the ferrogel is observed perpendicular to the applied magnetic field.