Experimental and Constitutive Modelling of Viscoelastic Responses in Carbon Black-Filled Natural Rubber Under Cyclic and Relaxation Loading

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Abstract
Elastomeric materials exhibit complex time-dependent behaviour under mechanical loading, necessitating accurate constitutive models for industrial applications. This study investigates the hyperelastic and viscoelastic responses of two carbon black-filled natural rubber compounds (50 ShA and 60 ShA) through cyclic shear/compression tests and stress relaxation experiments. The Arruda–Boyce model captures equilibrium behaviour, while the Bergström–Boyce model predicts transient viscoelasticity without relying on Prony series. Considering the results obtained it can be concluded that quantitative hysteresis analysis shows 7–26% energy dissipation, dependent on hardness and strain rate. Relaxation rates (10−6–10−7 s−1) inversely correlated with hysteresis, validated by FEM simulations. A deviation of <3.5% between experiments and simulations confirms the model’s robustness for long-term viscoelastic predictions. This framework enables the efficient design of rubber components (e.g., seismic isolators, seals) requiring prolonged durability under load.

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