Experimental study and numerical simulation of short- and long-term shear stress relaxation behaviors of magnetorheological elastomers

An experimental study and numerical simulation of short- and long-term shear stress relaxation behaviors of nonaligned and aligned magnetorheological elastomers (MREs) were investigated. The aligned MRE was created by aligning micro-size carbonyl iron particles in chains in silicon rubber using an external magnetic field during the curing process, while the nonaligned MRE was fabricated without applying a magnetic field. The effects of permanent magnetic fields on the shear stress relaxation of the nonaligned and aligned MREs were examined using the double-lap shear stress relaxation test with a short-term period of 1200 s and a long-term period of \(1.08 \times 10^{6}\text{ s}\). The shear stress and relaxation modulus of the nonaligned and aligned MREs increased considerably with the rise of magnetic flux density to about 500 mT and then enhanced slightly above 500 mT. The shear stress and relaxation modulus of the aligned MRE were considerably higher than those of the nonaligned one. The shear stress relaxation of the nonaligned and aligned MREs was numerically simulated using the fractional derivative viscoelastic Kelvin–Voigt model. The model parameters were identified by fitting the relaxation modulus to the short-term measured data of the MREs. The shear stress estimated from the investigated model with fitted parameters was in excellent agreement with the short-term experimental data of the MREs measured under different magnetic fields. Besides, the short-term model-fitted parameters were used to predict the long-term shear stress relaxation of the nonaligned and aligned MREs. The largest difference between model-predicted and long-term measured results for the nonaligned and aligned MREs was less than 1%. Therefore, the studied model can be used to predict the long-term shear stress relaxation of the nonaligned and aligned MREs.