Linear magneto-viscoelastic model based on magnetic permeability components for anisotropic magnetorheological elastomers

Highlights: • A new magnetic model for anisotropic MREs dependent on magnetic permeability is presented. • Magnetic permeability components of anisotropic MREs were measured and modelled. • The magneto-viscoelasticity was modelled in a single model. • Magneto-viscoelastic model was extended in the frequency and magnetic field domain. • All the work was done in the linear viscoelastic region. A new magneto-viscoelastic model is presented for anisotropic magnetorheological elastomers (MREs), which combines the dynamic behaviour and magnetic permeability components. Five samples were synthesised with different particle contents. Dynamic properties were measured using a rheometer equipped with a magnetorheological cell. A four-parameter fractional derivative model was used to describe MRE viscoelasticity in the absence of a magnetic field. The magnetic permeability of each sample was measured with a vibrating sample magnetometer. From experimental measurements of longitudinal and transverse components of the magnetic permeability, the dependency with magnetic field was modelled. The new magneto-induced modulus model proposed in this work is based on the model developed by López-López et al. [19] for magnetorheological fluids, and was adapted for anisotropic MREs. The proposed model includes the longitudinal and transverse components of magnetic permeability, and it is valid for the linear viscoelastic region of anisotropic MREs. The errors between experimental values and the values predicted by the model do not exceed 10%. Hence, a new linear magneto-viscoelastic model for anisotropic MREs is developed, which predicts the effect of magnetic field on the dynamic shear modulus as a function of magnetic field intensity and frequency.