A time varying system perspective on rubber mount tests

Abstract

Rubber tests typically only consider the first harmonic of responses and thus ignore additional information about variation of properties during a cycle. The Payne effect is then only described as a decrease of modulus with amplitude. An harmonic modulation is introduced as a novel way to look at the classical harmonic balance characterization of periodic signals in an effort to answer the question of when in the period is the system close to being linear ? In the case of enforced displacement tests, the harmonic modulation of force signals corresponds to an instant material stiffness or instant modulus. Sine test results are thus interpreted as trajectories in a complex modulus / strain plane that are much more discriminating than the traditional representation as a complex modulus and gives indication of coupling between hyperelastic, hysteretic and viscoelastic behaviors. This new interpretation of classical results is shown to be relevant as a correlation tool and a constitutive model for rubber is validated in its ability to reproduce the instant modulus behavior in a wide range of cases.