### Aims and Contents  
The summary presented in the above subsection has shown that the behavior of the elastomeric bearings is influenced by numerous factors that often interact in a complex way. Although the influence of lateral displacement and axial loads have been well described, only few scientific works are currently available regarding the influence of the tension on the response of base-isolated structures. Moreover, no significant efforts were made to combine the results of the aforementioned research works in a single model and to evaluate its influence on the nonlinear response of base-isolated structures. In the present work a unified modelling of the high damping rubber bearings (HDRBs), able to take into account for the effects of tension loads together with other important nonlinear phenomena which affect these devices, is introduced. It exploits the findings of well-established theoretical studies, numerical simulations, and experimental tests available in the scientific literature. The most promising results presented in different works are used by the authors to correct and improve the classical linear modelling of the HDRBs so that it also includes the influences of different nonlinear phenomena. To this end, the constant stiffnesses of the viscoelastic linear model, usually adopted to predict the seismic response of base-isolated buildings, are modified by applying four additional parameters. Specifically, the horizontal linear stiffness at shear zero strain is corrected, multiplying its original expression with two parameters, resulting from the research works presented in [13; 15]. The latter leads to a nonlinear expression of the horizontal stiffness which includes the effects of both axial-load and lateral displacements. In a similar way, the rotational stiffness at shear zero strain is corrected, multiplying its original linear expression as proposed in [15], while the nonlinear expression of the vertical stiffness at shear zero strain is obtained modifying the original stiffness at shear zero strain as suggested in [32]. This work accounts for effects of lateral displacement, cyclic vertical and horizontal loading and cavitation and post-cavitation phenomena. Reliability and accuracy of the proposed model are investigated by a series of numerical simulations in which the response of both the superstructure and base-isolation system are compared with that obtained by a simplified viscoelastic model and less sophisticated nonlinear models. In particular, nonlinear incremental dynamic analyses of three office buildings with three-, seven- and ten-storeys, all designed in compliance with the NTC18 Italian seismic code, are carried out by using a finite element computer code, developed by the authors. In this specially designed software, the nonlinear response of the superstructure is modeled by the lumped plasticity model proposed in [34; 35] while the nonlinear behavior of the HDRBs is simulated by the aforementioned models. As for the seismic input, three near-fault earthquakes (EQs) are selected from the PEER database [36; 37], one with prevailing horizontal component, characterized by long-duration horizontal velocity pulses, one with prevailing vertical component, characterized by high values of the ratio between peak values of the vertical and horizontal ground accelerations,and one with comparable horizontal and vertical components. To quantify the influence of the tension loads on the seismic response of the test structures, maximum ductility demands of r.c. frame members and total shear deformations, critical and cavitation loads of the HDRBs are evaluated comparing results obtained considering the proposed numerical model and other models of the HDRBs. These comparisons allow to define the situations where the use of the unified model is recommended to design both superstructure and isolators in a conservative way. A detailed presentation of the model developed by the authors to describe the nonlinear response of the HDRBs is shown in Section 2.