Equivalent rheological and restoring force models for predicting the harmonic response of elastomer specimens

Abstract This article presents two theoretical approaches that simulate the visco-elastic behaviour of elastomer specimens. The first approach, based on an equivalent rheological model, provides a dynamic modulus extracted from a Volterra development of the visco-elastic constitutive law using either relaxation or creep kernels. The second approach establishes a restoring force model based on a first-order differential equation that relates the restoring force to the deflection, the forcing frequency and deflection amplitude dependence being taken into account by the envelope curves of the force–deflection loop. The two models proposed are first applied to an elastomer cylinder mount made of a small quantity of carbon black filler and then to elastomer plates made of a large quantity of black filler. The cylinder and plates specimens are subjected to traction–compression and shear tests, respectively. In order to compare the two approaches, the dynamic modulus of the second approach is extracted by applying classical formulae to the force–deflection loop obtained with the restoring force model. Moreover experimental investigations permit comparing the simulated and measured dynamic modulus and validating the two theoretical approaches proposed.