Unified parameter identification and dynamic response (PSD) modeling of hyper-elastic materials

Hyper-elastic materials such as silicone rubber and vulcanized natural rubber show strong nonlinear stress–strain behavior. Because of this, finding one consistent set of material parameters is difficult. In most cases, uniaxial, biaxial, and shear tests produce different Mooney–Rivlin constants. This limits how well the model can predict behavior under various loading conditions. In this study, a simple and unified form of the two-parameter Mooney–Rivlin model is proposed. It combines test-specific parameters into one common set that works for all loading modes. The method uses empirical averaging and validation through finite element simulations in ANSYS. Two materials, silicone and vulcanized natural rubber, are tested to check the accuracy of the approach. The unified parameters reproduce the experimental stress–strain curves with less than 10 % deviation across uniaxial, biaxial, and shear conditions. Dynamic response under random vibration is also studied using Power Spectral Density (PSD) analysis. At 1.1875 % strain, the peak PSD reaches 80.6 Stress 2 Hz −1 and shifts with pre-strain, showing a clear change with frequency. The model, though simple, captures the main features of both static and dynamic behavior while keeping the computation light. The findings show that this strategy provides a practical complement to more complex identification frameworks, offering a robust and data-efficient modeling tool when experimental information is limited. This unified Mooney–Rivlin approach offers a practical way to model elastomeric parts used in soft robotics, biomedical devices, and impact-absorbing structures. • Unified Mooney-Rivlin model delivers consistent accuracy in uniaxial, biaxial, and shear modes. • A single parameter set effectively captures the behavior of silicone and natural rubber. • Peak PSD reaches 80.6 Stress 2 /Hz at 1.1875 % strain, shifting predictably with pre-strain. • Finite-element simulations confirm strong agreement across all deformation modes. • Compact hyper-elastic model supports soft-robotic and biomedical component design.