A continuum magneto-mechanical model for magnetorheological elastomers

Magnetorheological elastomers (MREs) consist of micron-sized magnetizable particles embedded in a rubber matrix. Properties of these magneto-sensitive materials are changed reversibly upon application of external magnetic fields. They exhibit highly non-linear magneto-mechanical response which allows developing new devices and applications. However, the coupled magneto-mechanical behavior makes mathematical modeling of MREs quite complicated. So development of a reliable constitutive framework is essential for further understanding of this coupled behavior as well as simulation of the systems that utilize MREs. In this paper, a finite strain continuum model is developed for MREs where the effect of magnetization on material stiffness is directly introduced in the material shear modulus. It is shown that this approach simplifies the constitutive models and also perceives the magnetic saturation of MREs. Moreover, the coupled effects of magnetization, deformation and particle-chains orientation on the mechanical response are also taken into account in the introduced parameter. This reduces the number of material parameters, the required experimental tests for parameters identification and also simplifies the mathematical formulation of the developed constitutive equations which is beneficial for numerical formulations. A systematic two-step method is then introduced for material parameters identification which assures uniqueness of the parameters set. The predictive capabilities of the proposed model are examined via available mechanical and magneto-mechanical experimental data on both isotropic and anisotropic MRE samples at different configurations of magnetic field and loading with respect to the preferred direction of the samples. It is shown that the model can well predict the magneto-mechanical response of MREs at different deformation modes and magnetic fields.