Multi-scale modeling on tensile modulus of magnetorheological elastomers

Abstract

We have investigated the tensile modulus of structured magnetorheological elastomers (MREs) to understand their anisotropic properties in terms of spatial configuration of particles, particle volume fraction and magnetization density. A micromechanical model incorporated into the macroscopic constitutive laws was derived from the equivalent effective medium theory by considering the anisotropy of structured MREs. A three-parameter microscopic representative volume element was constructed to describe the microstructure of MREs in which the magnetic particles were arranged in the matrix forming layer or chain structure. By considering the transverse isotropic of the pure tensile modulus, we established a relationship between tensile modulus of magnetic-induced stress and mechanical strain, which can derive the tensile modulus of structured MRE in two directions under uniform magnetic field. The theoretical analysis showed that the field-response effect of the tensile modulus of MRE was dependent on the magneto-induced stress, magneto-induced spatial structure and far-field strain. Considering the particle interaction force in the presence of a magnetic field under tensile stress, we found that when the magneto-induced stress decreases with mechanic strain, the positive MR effect is generated, while the magneto-induced stress increases with mechanical strain, the negative MR effect is generated. Simulation results show that there is an optimal particles' volume fraction for structured MRE, in which the changing rate of tensile modulus is the largest in one direction. We evaluated the anisotropy of MREs by showing the ratio of Ez/Ex for both chain and layer structures as a function of magnetic field strength and particle fractions. The anisotropy of MRE with chain structure is most evident with the particles loading of 17.04%, in the absence of magnetic field and the anisotropy of MRE with layer structure reaches peak with the particles loading of 23.3%. When the magnetic field is applied, the anisotropy of MRE with chain structure is weakened and that with layer structure is enhanced with the particles loading lower than 10.1%. When the particles' volume fraction is higher than 10.1%, the anisotropy of both layer structure and chain structure of MRE is reinforced.