A visoelastic constitutive model for magneto-mechanical coupling of magnetorheological elastomers

This paper focuses on the behavior of field-dependent viscoelasticity for magnetorheological elastomers (MREs). A novel nonlinear constitutive model for magneto-viscoelastic behavior of MREs is proposed. The model considered here is thermodynamically motivated and based on the second law. An extended three-parameter standard linear solid model is proposed to describe the viscoelastic behavior of MREs, where the effect of particles on the elastomers at zero field is taken into account. Furthermore, the nonlinear magnetization and the local magnetic field within the ferromagnetic particle are incorporated to describe field-dependent constitutive behavior based on the dipole model. Then a set of analytical expressions of the constitutive law for MREs are obtained, and the parameters appearing in the model can be determined by those measurable experiments in mechanics and physics. The quantitative results demonstrate that this model can well capture the constitutive relation under both quasi-static and dynamic shear loading.