Visco-hyperelastic model for filled rubbers used in vibration isolation

The short time and cyclic behavior of filled rubbers used in vibration isolation in the frequency range 10(-2) to 10(2) rad/s is examined. A form of the free-energy function consistent with the assumption of an additive stress decomposition is employed. A constitutive law for the inelastic part of the stress is provided, in the form of an integro-differential equation, which involves the fractional order derivative of the internal variable. It is assumed that the volumetric response of the material is elastic. The elasticity of rubber is modeled following classical models (e.g., Rivlin, Ogden), extended to include compressibility. Step-by-step integration of the constitutive law is performed. Simple shear experiments are used to assess the capability of the model to capture essential response characteristics, such as stiffness reduction under cyclic loading of increasing amplitude and the variation of dissipated energy with amplitude and frequency.