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.