Simulation of a Truck Tyre Using a Viscoplastic Constitutive Rubber Model

Tyres are a vital component for handling and load carrying while also contributing to the operating cost and environmental impact. The innovations in tyre design are driven by the need to reduce greenhouse gases and to make a better compromise between conflicting tyre properties. To accurately simulate tyres and to make these compromises a representative rubber model needs to be incorporated with strain amplitude dependency for the storage and loss modulus (the Fletcher-Gent effect). Prony series is a commonly used viscoelastic model in tyre simulations but it does not take into account the Fletcher-Gent effect and e.g. possible nonlinearities due to axle load variations are not feasible to simulate. The Fletcher-Gent effect can be modelled using parallel rheological framework (PRF), which can consist of any combination of parallel material models. Nonlinear viscoelastic models have strain amplitude dependency for the storage modulus but single nonlinear parameters lose their clarity in a PRF. Another approach is to combine a linear viscoelastic model with plasticity as is done in this article. Here, an FE truck tyre is developed and used with a viscoplastic PRF model that utilises Prony series with Mooney-Rivlin hyperelasticity and multiple plastic networks. The benefit of this combination is that the strain amplitude and frequency dependency of the storage and loss modulus are separated, which makes parameter studies simpler. The article shows that an FE truck tyre with a viscoplastic PRF model can be used in different simulations to study e.g. steady-state rolling, footprint, vertical stiffness and longitudinal tyre forces.