A visco-elastic-plastic constitutive model of isotropic magneto-sensitive rubber with amplitude, frequency and magnetic dependency

Abstract

A three-dimensional visco-elastic-plastic constitutive model of isotropic magneto-sensitive (MS) rubber with amplitude, frequency and magnetic dependency under a continuum constitutive framework is developed. MS rubber is a kind of smart material mainly composed of a rubber matrix and magnetizable particles. Under a magnetic field, there is an increase of its dynamic modulus due to the interaction between the magnetic field and MS rubber, which is often referred to as the magnetic dependency of MS rubber. Experimental results reveal that besides the magnetic dependency, there is a frequency and amplitude dependency of its dynamic modulus. In specific, the modulus of MS rubber increases with increasing frequency and dereases with increasing strain amplitude. To depict the above properties and to consider the balance of energy in continuum mechanics framework, a new constitutive model consisting of a viscoelastic fractional derivative element, a bounding surface model in series with a neo-Hookean elastic model with magnetic sensitivity and a magnetic stress tensor term for MS rubber is proposed. The contribution of this constitutive model is that by using a free energy based method, with only eight material parameters, the amplitude, frequency and magnetic dependency of MS rubber can be reflected. After parameter identification, the simulation results show a good agreement with those of measurements. Therefore, by utilizing the model proposed, the ability of approaching the dynamic behavior of MS rubber-based vibration reduction devices in the design phase is possible which contributes to the application of MS rubber in noise and vibration reduction area.