Hyper-viscoelastic constitutive models for predicting the material behavior of polyurethane under varying strain rates and uniaxial tensile loading

Non-linearity, loading rate, as well as temperature and pressure dependency present major challenges in the investigation of properties, particularly the mechanical properties of elastomeric polymers. Recently, material and structural engineers have focused on investigating the mechanical behavior of hyper-elastic materials under varying strain rate conditions. In addition, they have been developing constitutive models to define the non-linear behavior of these materials, combined with the strain rate effect, which simulates behavior under different loading conditions. In this study, a new viscoelastic model is proposed to simulate the variation in the mechanical properties of elastomeric materials. Hyper-viscoelastic constitutive models were also developed by modifying existing hyper-elastic models (Mooney–Rivlin and Ogden) with existing viscoplastic models (Cowper–Symonds and Johnson–Cook) and the proposed viscoelastic model. The proposed models were verified through experimental results by investigating the uniaxial tensile behavior of an elastomeric polyurethane (PU) sample under varying low strain rate regimes (0.001 s⁻¹–0.1 s⁻¹). The proposed viscoelastic model exhibited the best correlation to present the enhancement of mechanical properties under varying strain rate conditions compared with the Cowper–Symonds and Johnson–Cook models. The proposed hyper-viscoelastic models could be used to predict material behavior using only one set of hyper-elastic model parameters at a certain strain rate, combined with viscoelastic model parameters. The hyper-viscoelastic cumulative strain energy and stress–strain models, which were developed with the proposed viscoelastic model, demonstrated high accuracy in predicting material behavior with the strain rate effect of elastomeric PU or similar materials.