A nonlinear constitutive model by spring, fractional derivative and modified bounding surface model to represent the amplitude, frequency and the magnetic dependency for Magneto-sensitive rubber

Magneto-sensitive (MS) rubber is a kind of smart material mainly consisting of magnetizable particles and rubber. Inspired by experimental observation that the shear modulus for MS rubber is strongly dependent on amplitude, frequency and magnetic field; while the impact for the magnetic field and strain to the loss factor is relatively small, a new nonlinear constitutive model for MS rubber is presented. It consists of a fractional viscoelastic model, an elastic model and a bounding surface model with parameters sensitive to the magnetic field. To our knowledge, it is the first time that the bounding surface model is incorporated with the magnetic sensitivity and used to predict the mechanical properties for MS rubber. After comparison with the measurement results, it is found that the shear modulus and the loss factor derived from the simulation fit well with the experimental data. This new constitutive model with only eight parameters can be utilized to describe the amplitude, frequency and the magnetic field dependence for MS rubber. It provides a possible new way to understand the mechanical behavior for MS rubber. More importantly, the constitutive model with an accurate prediction property for the dynamic performance of MS rubber is of interest for MS rubber applications in noise and vibration reduction area.