A simplified methodology to predict the dynamic stiffness of carbon-black filled rubber isolators using a finite element code

A new and different approach to the inclusion of the amplitude-dependent effect, known as the Fletcher–Gent effect or Payne effect, in a linear viscoelastic rubber material model is presented to predict the dynamic stiffness of filled rubber isolators using a finite element (FE) code. The technique is based on providing a linear viscoelastic model with the adequate material data set, once the dynamic strain amplitude, to which the rubber mount is subjected, is estimated. A generalized Zener model is adopted to describe the frequency-dependent behaviour of the material through the use of hereditary integrals. The dynamic strain amplitude dependence is not modelled through any friction model or plasticity theory, as usually is in literature. It is introduced by considering the frequency-dependent properties of the compound at an adequate strain value, which enforces the estimation of an equivalent strain value. As a first approximation, a quasi-static value is used as the reference value at which material properties should be provided to the linear viscoelastic model. The technique works directly in frequency domain, the dynamic stiffness of the bushing being directly obtained. The methodology is applied to evaluate the dynamic stiffness of a real bushing in working conditions with very satisfactory results. Despite the assumptions made, especially regarding the estimation of the equivalent strain amplitude value, errors of the predictions fall within the limits usually accepted by rubber manufacturers.