Bidirectional modelling of high-damping rubber bearings

High-damping rubber (HDR) bearings are used in seismic isolation applications for buildings and bridges, although no models are currently available for the accurate description of the shear force-deformation response under bidirectional loading. A strain rate-independent, phenomenological model is presented which effectively represents the stiffness, damping, and degradation response of HDR bearings. The model decomposes the resisting force vector as the sum of an elastic component in the direction of the displacement vector and a hysteretic force component parallel to the velocity vector. The elastic component is obtained from a generalised Mooney-Rivlin strain energy function, and the hysteretic component is described by an approach similar to bounding surface plasticity. Degradation is decomposed into long term ("scragging") and short term ("Mullins' effect") components. Calibration is carried out over a series of bidirectional test data, and the model is shown to provide a good match of slow strain-rate experimental data using a unique set of material parameters for all tests. A testing protocol and calibration of the model for use in design of structures with HDR bearings are discussed.