High damping rubber (HDR) bearings are extensively used in seismic design for bridges due to their remarkable energy dissipation capabilities, which is critical during earthquakes. A thorough assessment of crucial factors such as temperature, rate, experienced maximum amplitude, and the Mullins effect of HDR on the mechanics-based constitutive model of HDR is lacking. To address this issue, we propose a deep learning approach that integrates the Gate Recurrent Unit (GRU) and attention mechanism to identify time series characteristics from compression-shear test data of HDR specimens. It is shown that the combination of GRU and attention mechanism enables accurate prediction of the mechanical behavior of HDR specimens. Compared to the sole use of GRU, this suggested method significantly reduces model complexity and computation time while maintaining good prediction performance. Therefore, it offers a new approach to constructing the HDR constitutive model. Finally, the HDR constitutive model was used to analyze the impact of experienced maximum amplitudes and cycles on following processes. It was observed that maximum amplitudes directly influence the stress-strain relationship of HDR during subsequent processes. Consequently, a solid foundation is laid for evaluating the responses of HDR bearings under earthquakes.

The complex mechanical properties of high-damping rubber (HDR), a commonly used seismic isolation material in buildings and bridges, present a significant challenge in civil engineering. In a previous study, the authors proposed an HDR constitutive model that combines a Gated Recurrent Unit (GRU) and an attention mechanism, offering novel insights into the mechanical properties of HDR. The constitutive model was simplified first to facilitate the deployment of the proposed constitutive model within the finite element analysis environment. Then, the simplified constitutive model was converted into a uniaxial material format suitable for use within the open system for earthquake engineering simulation (OpenSees). In OpenSees, the uniaxial material was named HDRGA material, and the code for the HDRGA material header and source files was written. Finally, an HDR surrogate constitutive model was developed in OpenSees. To validate the precision of the HDRGA material in characterizing the mechanical attributes of HDR, a two-node model and a single-pier model were devised, and their accuracy was verified through a comparative analysis of test results and nonlinear time history calculation results, respectively. The results demonstrate that the developed HDRGA material is capable of performing well under earthquakes.

Factors affecting the mechanical properties of the high-damping rubber plate mainly include temperature, shear strain rate, shear strain amplitude, and compressive stress. However, the existing studies focused on one factor and have not conducted detailed research on the coupling relationships between various factors. The influence on the mechanical properties of the high-damping rubber plate of one factor will change with the change in other factors. To study the coupling correlation, a series of horizontal cyclic loading tests were designed and carried out. Due to the simultaneous hyperelastic and viscoelastic properties of high-damping rubber, the hysteresis curve of the high-damping rubber plate is decomposed into a hyperelastic part and a damping part. Equations of the two parts are deduced by a theoretical method, and all the coefficients of the two parts are obtained by fitting the test results. Then, the variation coefficient is used to study the influence degree of each factor on these coefficients. Finally, the correlation variation coefficient is defined as the variation coefficient of variation coefficients and is used to quantify the coupling correlation between the factors. This study is of great significance in exploring the coupling correlation between the factors affecting the mechanical properties of the high-damping rubber plate.