Multiaxial Behaviors of Laminated Rubber Bearings and Their Modeling. II: Modeling

Mathematical models of laminated rubber bearings under multiaxial loading are proposed on the basis of the experimental data in the accompanying paper. First, a one-dimensional model of the bearings is proposed. In this model, an elastoplastic model is extended by adding the displacement-dependent isotropic hardening rule and the parallel nonlinear elastic spring. Furthermore, the equivalent stiffness and damping ratio of the model are derived in the analytical forms, which are useful for the design. Second, the three-dimensional constitutive law is simplified by considering the biaxial simple shear deformation to derive the two-dimensional elastoplastic model. Then, this model is extended by a similar way as in the one-dimensional case to obtain the two-dimensional model of the bearings. The proposed models are shown to well reproduce the experimental results. Third, to confirm the ability of the proposed models to predict the seismic response, a triaxial hybrid seismic response experiment is conducted. In comparison with the experimental results, the simulations by the proposed model are found to accurately predict the response of the experiment.