On the modelling of nonlinear viscoelastic relation for rubber-like materials

Abstract

A large class of dissipative materials are modelled using a time- and frequency-dependent viscoelastic relations. A typical class of such materials are rubber which finds application in automotive tires, air springs etc. One of the most interesting effects that rubber exhibits are the nonlinear rate-dependent behaviour, which is linked to the Payne effect. It is found that the reinforced rubber under monotonically increasing strain amplitude results in decreasing storage and a sigmoidal-shaped loss modulus. In this study, we propose a phenomenological hyper-viscoelastic model that consists of a hyperelastic element connected in parallel with another hyperelastic component in series with a non-linear viscoelastic flow element. As a fundamental concept, we split the total stress into an elastic and a history-dependent component. As an example problem, we model the constitutive response of a rubber sample where the results have shown a perceptible distinction between the linear and nonlinear formulations. It can be said that from the practical point of view, the linear viscoelastic formulation is simple and reasonable to use only for small strains. We conclude this paper by applying a constant pre-strain amplitude with a different frequency of loading.