Magnetoactive elastomers (MAEs) are emerging smart materials, which exhibit rapid and reversible variations in the viscoelastic properties under an applied magnetic field. While response behaviors of these novel materials have been widely studied using phenomenological based approaches, only a few studies have attempted the physics based analyses of MAEs. The main aim of the present thesis research is to develop a continuum based formulation considering the magneto-elastic coupling for predicting the quasi-static behavior of both the isotropic and anisotropic MAEs undergoing small and finite deformations. Firstly, the constitutive magneto-mechanical equations for an isotropic magnetoactive medium are formulated considering the principle of material objectivity. A stored energy density function has been introduced with respect to the invariants of the Cauchy-Green deformation tensor and the magnetic field induction vector. The proposed function is subsequently used to develop a material model for finite deformation analysis of the isotropic MAEs. A linearization scheme has also been implemented to formulate a small-deformation theory for the isotropic material.
In the second part, a novel energy density function for an incompressible transversely-isotropic deformable magnetic solid has been presented in terms of some invariants based on both the mechanical and magnetic anisotropy. The proposed energy density function is effectively used to formulate a coupled magneto-elastic model of the transversely-isotropic MAEs. 
The validity of the proposed models is demonstrated through comparisons of the model responses with the laboratory measured characteristics. For this purpose, the isotropic and transversely-isotropic cylindrical MAEs were fabricated in the laboratory by mixing silicon rubber with micron-sized carbonyl iron particles (15% volume fraction). The mixture was cured in the absence and presence of the external magnetic field, respectively, to realize isotropic and anisotropic structures. An experimental set-up was designed to accurately measure the relative permeability of the isotropic and anisotropic samples. The torsion-deflection characteristics of the MAEs were also measured under varying applied magnetic field by utilizing a magneto-rheometer.
The measured data were used to examine validity of the proposed models and to identify parameters of constitutive equations for both the isotropic and anisotropic MAEs. The comparison revealed reasonably good agreements between the analytical and experimental results. The proposed models could thus serve as essential tools for designing MAE-based devices for noise and vibration control applications.