Micromechanical analysis on tensile modulus of structured magneto-rheological elastomer

This paper proposed a micromechanical model to investigate the tensile modulus of structured magnetorheological elastomers (MRE) to understand its anisotropic properties. A three parameter representative volume element (RVE) model was presented to describe the microscopic structure, where particles could be organized in layer-like or chain-like structure. And the tensile modulus is defined as a ratio of stress to strain in the stretched direction. We then applied effective medium theory to derive a theoretical model for the modulus of MRE in the absence of magnetic field, considering the influence of particles configuration and volume fraction. In addition, the effect of magnetic field on magneto-induced stress inside MRE is evaluated to further establish a multi-scale model which explains the magneto-rheological effect of structured MRE. The proposed model was then compared with finite element analysis and 'free energy' model. It demonstrated that the proposed model match better with the finite element solutions than that of 'free energy' method. The advantage of the proposed model is that it couples the magnetic field and displacement field, and considers the influence of both particles spatial energy and the relative position on magneto-rheological effect. The stiffer or softer of MREs induced by an applied magnetic field under tensile stress is predicted that is conformed to previous studies.