Numerical simulation of single- and multi-step shear stress relaxations of isotropic magnetorheological elastomer using fractional derivative viscoelastic models

The paper presents numerical simulations of single- and multi-step shear stress relaxations of isotropic magnetorheological elastomer (MRE) using fractional derivative Maxwell and Kelvin–Voigt viscoelastic models. The isotropic MRE has been fabricated by filling micro-sized carbonyl iron particles in silicone rubber. Fractional derivative Maxwell and Kelvin–Voigt viscoelastic models were used to fit the experimental data of the isotropic MRE measured by single- and multi-step relaxation tests at different constant strains and external magnetic fields. The fractional Maxwell viscoelastic model showed a relatively large difference between the measured and calculated results. The fractional Kelvin–Voigt model was fitted well with the experimental data of the isotropic MRE at various constant strain levels under different magnetic fields in both single- and multi-step shear stress relaxations. The calculated shear stress with the long-term prediction is in excellent agreement with the measured one. Therefore, the fractional derivative Kelvin–Voigt viscoelastic model is applicable to predict the long-term stress relaxation of the isotropic MRE.