Novel hyper-viscoelastic approach to modelling elastomer mechanic behaviour with relaxation spectrum

Elastomers, such as polyurethane, exhibit hyperelastic behaviour and distinct rate dependence under a wide range of strain rates. Herein, a methodology for developing a hyper-viscoelastic constitutive model for succinctly characterising the mechanical behaviour of polyurethane under large deformations and a wide range of strain rates is proposed. The model is constructed using a long-term hyperelastic formulation combined with a rate-dependent viscoelastic model. This model is based on internal state variables and a finite strain formulation. A polyurethane elastomer was used as a sample to develop this model, by way of testing wide strain-rate mechanical behaviour (0.001–5000s⁻¹) and viscoelastic behaviour. The viscoelastic behaviour was obtained using the equivalent time–temperature superposition relation. A parameter-fitting algorithm was adopted to separate the long-term behaviour from the viscoelastic behaviour. The long-term behaviour was modelled using a Mooney–Rivlin hyperelastic model, and its parameters were identified using the least-squares method. The time-dependent viscous effect calculated using the Prony series-based model was approximately determined based on the continuous relaxation spectrum. The characterisation capacity was confirmed through a thorough comparison with experimental curves. This model can be extended to other elastomers, even under tension, without any specific limitations of the internal components.