Microstructure-based modeling of magneto-rheological elastomers

Filled with iron particles, polymers can be made responsive to magnetic fields. Specifically, the elastomers that change stiffness in response to a magnetic field are usually called magneto-rheological elastomers (MREs). Anisotropic MREs, in which the particles are aligned during curing and form chain-like structures, exhibit a more significant magneto-rheological (MR) effect, i.e. the field-induced stiffening. In this paper, we first develop a constitutive model for the nonlinear behavior of deformable solids under magnetic field. Based on the filler-substrate microstructure of MREs, we further implement the theory into a finite element method. The magneto-mechanical response of a representative unit cell of MRE is studied using the finite element method. The MR effect in both the shear modulus and the tensile modulus of an MRE is studied. In addition, we consider the viscoelasticity of the polymer matrix and study its effect on the properties of an MRE. Using the viscoelastic model for MRE, we also investigate the frequency dependence of the MR effect.