Magnetorheological elastomer (MRE) is a kind of smart material fabricated by embedding magnetizable particles into polymer matrix. Under a magnetic field and mechanical loadings, the modulus of MRE changes rapidly, reversibly and continuously, which offers a wide application potential in vibration control area. The dynamic behavior of isotropic MRE shows the strong frequency, strain amplitude and magnetic dependence. However, the nonlinear dynamic behavior of isotropic MRE only receives few theoretical attentions and there is a certain gap between experimental testing and constitutive modeling.
In this manuscript, firstly, the magnetic dependent nonlinear behavior of isotropic MRE is demonstrated through the quasi-static and dynamic tests. In order to evaluate the dynamic performance of isotropic MRE accurately and guide the design of products based on isotropic MRE, a new constitutive model of isotropic MRE is developed based on continuum mechanics theory. Subsequently, a numerical implementation algorithm is applied to parameter identification of the model based on experiment results. Figure 1 and Figure 2 are dynamic hysteresis stress-strain responses of isotropic MRE under the magnetic field strength of 0 and 0.4 T, which shows that the proposed model can describe the modulus magnetic stiffening effect and the magnetic dependent nonlinear dynamic behavior of isotropic MRE with accuracy.
Finally, the prediction ability of the model is examined. In Figure 3, obviously, the stress relaxation curves indicate that a larger peak stress is exhibited if a faster strain rate is applied. Furthermore, it can be found that the peak stress increases as the magnetic field strength increases, which verified again the validity of the model to replicate the modulus magnetic stiffening effect. Besides, in Figure 4, the stress-strain curves of isotropic MRE show that a faster loading rate leads to a larger peak stress and more energy dissipation. Moreover, due to the nonlinearity, the peak stress does not increase proportionally to the strain amplitude, which is caused by the strain amplitude dependent viscosity evolution law utilized in constitutive equation.