Experimental and theoretical study of temperature-dependent variable stiffness of magnetorheological elastomers

The magnetorheological properties of a series of magnetorheological elastomers with ferromagnetic particles of different mass fractions and different diameters are investigated. The aim is to provide a basis for the preparation of high-performance material. The shear behavior of the magnetorheological elastomers is also investigated as a function of temperature. The results essentially reveal the temperature-dependent nature of the variable stiffness of the magnetorheological elastomers. A modified Gauss distribution columnar model of ferromagnetic particles (with a temperature-dependent magnetic permeability) and a modified super-elastic rubber matrix (with a linear thermal expansion coefficient) is developed and used to explore the nature of the temperature-dependent variable stiffness. The results suggest that the interaction between the rubber matrix and ferromagnetic particles is the most critical factor responsible for the temperature dependence and not the features of the two components themselves. On the basis of System Identification Theory, a fitting polynomial is added to modify the constitutive model, which can represent the interaction between the rubber matrix and ferromagnetic particles. Polynomial data fitting and a theoretical model were used to derive an expression for the temperature dependence. As a result, the magnetic field-induced shear modulus was obtained as a semi-empirical model. This was then used to draw maps of the temperature-induced and magnetic field-induced shear modulus. The calculated results were compared with the experimental data and the errors found to be acceptable, which verifies the effectiveness and reliability of the semi-empirical model. Finally, the temperature dependence of the shear modulus is converted into the temperature dependence of the shear stiffness.