Dynamic Loading Effect on Incompressible Synthetic Rubber-Like Mooney-Rivlin and Neo-Hookean Strain-Energy Functions under Biaxial Tension

In engineering applications involving flexible components and load-bearing structures, rubber-like materials often experience large deformations and cyclic or time-dependent stresses. Accurately modelling their nonlinear mechanical behaviour under such conditions is crucial for reliable performance prediction. This study examines the response of hyperelastic materials subjected to dynamic biaxial loading using two classical strain-energy functions: the Neo-Hookean and Mooney–Rivlin models. The stress–strain response under biaxial tension was derived theoretically from finite deformation principles, and the models were evaluated at different loading rates and strain amplitudes. The Neo-Hookean model, with its single-parameter formulation, provided satisfactory predictions at small-to-moderate stretch ratios, where material behaviour remains nearly isotropic and linear deviations are minimal. However, at larger deformations, where stress anisotropy and nonlinearities become more significant, the Mooney–Rivlin model offered better accuracy due to its two-parameter formulation, which accounts for higher-order effects. The results further reveal that model choice influences the predicted stiffness of materials under dynamic loading, with potential consequences for fatigue resistance, structural stability, and energy absorption. These findings demonstrate the limitations of oversimplified constitutive laws and underscore the necessity of adopting multi-parameter models when dealing with complex stress states. Practical implications extend to engineering systems such as flexible membranes, vibration isolators, and sealing elements, where performance reliability depends on accurate representation of hyperelastic behaviour. Overall, this work highlights the importance of selecting appropriate constitutive models for the design, simulation, and optimisation of rubber-like materials under challenging stress and loading conditions