Global and local vertical stiffness of laminated rubber bearings under severe compression and lateral deformation

Previous studies mainly evaluated the global vertical stiffness (K_v) of laminated rubber bearings, typically considering the total vertical deformation as the sum of individual rubber layers. Under pure compression, maximum deformation occurs in the top layer. However, under combined axial pressure and lateral deformation, deformation distribution shifts, with the location of maximum deformation varying with lateral displacement magnitude among the rubber layers. Thus, evaluating the local K_v of each rubber layer is essential to accurately capture mechanical behavior. A layer-by-layer analysis identifies the most deformed layer under different lateral displacements, enabling determination of the minimum local K_v. Finite element simulations are significantly improved by incorporating the Mullins effect and Prony-series viscoelasticity into the Yeoh hyperelastic model, thereby capturing the full loading and unloading behavior and achieving strong agreement with experimental data. This study presents a comprehensive investigation into both the global and local K_v of rubber bearings, considering variations in the first and second shape factors (S₁ and S₂) and different axial pressure levels (P, 2P, and 3P), where P denotes the design pressure. The results indicate that increasing S₂ enhances global K_v but also leads to more severe degradation in local K_v. In contrast, higher S₁ values improve bearing stability and reduce the sensitivity of local K_v relative to global K_v. Bearings with low S₁ and high S₂ exhibit greater stiffness reduction under increasing axial pressure, while higher S₁ values mitigate this effect. Finally, empirical formulations for normalized global and local stiffness are proposed, showing good correlation with both finite element and experimental results.