Viscoelastic Parameter Model of Magnetorheological Elastomers Based on Abel Dashpot

Abstract

In this paper, a parametric constitutive model based on Abel dashpot is established in a simple form and with clear physical meaning to deduce the expression of dynamic mechanical modulus of MREs. Meanwhile, in consideration for the pressure stress on MREs in the experiment of shear mechanical properties or the application to vibration damper, some improvements are made on the particle chain model based on the coupled field. In addition, in order to verify the accuracy of the overall model, five groups of MREs samples based on silicone rubber with different volume fractions are prepared and the MCR51 rheometer is used to conduct the experiment of dynamic mechanical properties based on frequency and magnetic field scanning. Finally, experimental results indicate that the established model fits well with laboratory data; namely, the relationship between the dynamic modulus of MREs and changes in frequency and magnetic field is well described by the model.

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

“…2 The fractional derivative model can be used to decrease the number of material parameters, and these parameters have a physical meaning [11]. Using these advantages the viscoelastic behaviour of isotropic [7,12] and anisotropic [13,14] MREs have recently been modelled using fractional derivative models. Agirre-Olabide et al [12] have used four material parameters to simulate the viscoelastic behaviour of isotropic MREs and Xu et al [7] have combined a fractional Kelvin and Maxwell model in parallel configuration developing a higher order model (seven material parameters).…”

“…Agirre-Olabide et al [12] have used four material parameters to simulate the viscoelastic behaviour of isotropic MREs and Xu et al [7] have combined a fractional Kelvin and Maxwell model in parallel configuration developing a higher order model (seven material parameters). Guo et al [13] have combined an Abel dashpot (fractional derivative element) and a spring in a series configuration, while Zhu et al [14] have combined in a parallel configuration. Hence, three material parameters have been used to predict the viscoelastic behaviour of anisotropic MREs.…”

“…A classical four parameter magneto-viscoelastic model have been proposed by Li et al [24], and all material parameters were fitted to experimental data for each magnetic field densities. The magneto-viscoelastic behaviour using fractional derivatives have been modelled for isotropic [25] and anisotropic [13,14] MREs. Agirre-Olabide et al [25] have proposed a three-dimensional magneto-viscoelastic model within the linear viscoelastic region for isotropic MREs, coupling a fractional derivative based viscoelastic model with a magnetic field dependant model.…”

“…Agirre-Olabide et al [25] have proposed a three-dimensional magneto-viscoelastic model within the linear viscoelastic region for isotropic MREs, coupling a fractional derivative based viscoelastic model with a magnetic field dependant model. On the other hand, the magneto-viscoelastic model proposed in [13,14] for anisotropic MREs have combined in a serial configuration a fractional derivative Maxwell model and a spring, which is dependent on the magnetic field and modelled assuming chain-like structures. The strain amplitudes applied were 0.1% in [13] and 25% in [14].…”

“…On the other hand, the magneto-viscoelastic model proposed in [13,14] for anisotropic MREs have combined in a serial configuration a fractional derivative Maxwell model and a spring, which is dependent on the magnetic field and modelled assuming chain-like structures. The strain amplitudes applied were 0.1% in [13] and 25% in [14].…”