Constitutive model of isotropic magneto-sensitive rubber with amplitude, frequency, magnetic and temperature dependence under a continuum mechanics basis

• Published in: International journal of engineering science
• Main Authors: Wang, Bochao, Kari, Leif
• Format: Journal Article
• Language: English
• Published: 2020
• Subjects: Amplitude dependence; Continuum mechanic frame; Engineering Mechanics; Frequency dependence; Magnetic dependence; Magneto-sensitive rubber; Teknisk mekanik; Temperature dependence
• ISSN: 1879-2197; 0020-7225

A three-dimensional nonlinear constitutive model of the amplitude, frequency, magnetic and temperature-dependent mechanical properties of isotropic magneto-sensitive (MS) rubber is developed. The main components of MS rubberis an elastomer matrix and magnetizable particles. When a magnetic field is applied, the modulus of MS rubber increases, which is known as the magnetic dependence of MS rubber. In addition to the magnetic dependence, there arefrequency, amplitude and temperature dependencies of MS rubber. Specifically, a higher frequency, a smaller strain amplitude and a lower temperature lead to an increased magnitude of the dynamic modulus. To represent the above properties and to stimulate the possible application of MS rubber in the anti-vibration area, a continuum mechanic framework based constitutive model consisting of a fractional standard linear solid (SLS) element, an elastoplastic element and a magnetic stress term of MS rubber is developed. The frequency and amplitude dependencies are depicted by a fractional SLS element and an elastoplastic element, respectively. A hyperbolic tangent function with a scalar product of magnetic flux density as an independent variable is introduced to consider the magnetic dependence. Furthermore, the temperature dependence is taken into account by including the William-Landel-Ferry function and the Arrhenius function to the fractional SLS element and the elastoplastic element, respectively. The technical innovation of this constitutive model is that the amplitude, frequency, magnetic and temperature dependent mechanical properties of MS rubber are incorporated into a whole constitutive model under the continuum mechanics frame and based on the free energy assumption. Comparison between the simulation and measurement results in a wide frequency range with different levels of magnetic field, strain amplitude and temperature shows that the fitting effect of the developed model is very good. Therefore, the constitutive model proposed in this paper enables the prediction ofthe mechanical properties of MS rubber under various operating conditions with high accuracy, which will drive MS rubber’s application in engineering applications, especially in the area of MS rubber-based anti-vibration devices.