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.
Magneto-active polymers (MAPs), composed of polymer matrices and magnetic filler particles, are smart materials that
deform quickly in an external magnetic field. The ability to produce large deformation of MAPs makes these materials
promising for actuators and sensors. Due to the viscoelasticity of the polymer matrices, MAPs usually demonstrate ratedependent
dynamic properties. However, very few models of coupled magnetic field and viscoelasticity in MAPs exist
in the literature, and even fewer are capable of reliable predictions. Starting from nonequilibrium thermodynamics, a
field theory is developed to fully couple the finite-deformation viscoelasticity and magnetostatics of MAPs. The theory
provides a guideline for experimental characterization of MAPs, and most material laws are readily applicable in this
framework. A specific material model is prescribed for an idealized MAP. As demonstrations, numerical examples are
implemented on the responses of the MAP in response to both uniform and nonuniform magnetic fields. In the nonviscous
limit, our theory recovers a model for elastic MAPs, and is capable of capturing instability phenomena observed
in the experiments.
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