A Hysteresis Model of High-Damping Rubber Bearings Using an Integral Type Deformation History Constitutive Law

Abstract

A new hysteresis model for high-damping rubber bearings is proposed, which has been developed based on an elasto-plastic, integral type deformation history constitutive law. One of the characteristics of the proposed model is the applicability of the same material parameters as the proposed model to finite element method analyses. Firstly, we derive the horizontal biaxial hysteresis model from the elasto-plastic constitutive law. Next, we compare the results of numerical analyses using the proposed hysteresis model with experimental results for tests of high-damping rubber bearings subjected to horizontal biaxial loading, and verify the validity of the proposed model. Lastly, we perform finite element method analyses and numerical analyses using a multi-shear springs model, and the results from each of these cases are compared with results given by the proposed model.

Proposal of deformation history integral‐type hysteresis model considering performance change of high‐damping rubber bearings and verification using substructure real‐time online testing system for seismically isolated structure

“…where τ and γ are the shear stress and shear strain, respectively; γ max is the experienced maximum shear strain; t is the elapsed time from the start of loading; Γ is the cumulative value of the shear strain increment (e.g., in the case of one cycle loading with a maximum shear strain of 1, Γ is 4); a, b, n, g 1g n , l 1 -l n , θ, and β are material parameters (here, n is the number of plastic terms); and γ 0 , Γ 0 , and t 0 are variables for integration. The modeling reported by Kato et al 4 and Mori et al 9 differ slightly. Kato et al 4 did not model the damage function W, whereas Mori et al 9 did not model the term bγ 3 .…”

“…The modeling reported by Kato et al 4 and Mori et al 9 differ slightly. Kato et al 4 did not model the damage function W, whereas Mori et al 9 did not model the term bγ 3 . Thus, Equations ( 1)-(3) are applicable to both studies.…”

“…The conventional one-dimensional DHI model developed in a previous study 4,9 is expressed mathematically as follows:…”

“…The conventional one‐dimensional DHI model developed in a previous study 4,9 is expressed mathematically as follows:$$$$ \tau =W\left( a\gamma +b{\gamma}^3\right)+\sum \limits_{i=1}^n\left\{{g}_i{\int}_0^{\Gamma}\left(\gamma {\prime}^2-\frac{2}{3}{\gamma \gamma}^{\prime }+1\right){e}^{\frac{\Gamma -{\Gamma}^{\prime }}{l_i}}d{\Gamma}^{\prime}\right\} $$$$$$$$ \Gamma ={\int}_0^t\left|\frac{d\gamma}{{d t}^{\prime }}\right|{d t}^{\prime } $$$$ $$$$ W=\theta +\left(1-\theta \right){e}^{-\frac{\gamma_{\mathrm{max}}}{\beta }}, $$$$where τ and γ are the shear stress and shear strain, respectively; γ max is the experienced maximum shear strain; t is the elapsed time from the start of loading; Γ is the cumulative value of the shear strain increment (e.g., in the case of one cycle loading with a maximum shear strain of 1, Γ is 4); a , b , n , g 1 ‐ g n , l 1 ‐ l n , θ , and β are material parameters (here, n is the number of plastic terms); and γ′ , Γ ′ , and t′ are variables for integration. The modeling reported by Kato et al 4 . and Mori et al 9 .…”

“…Because the behavior of HDR is more complex than that of other RBs, researchers have proposed many hysteresis models 1–3 . Some authors have proposed a hysteresis model based on the DHI‐type elastic–plastic model (the DHI model hereinafter 4–8 ) for HDRs. The features of the DHI model are as follows: The DHI model can reflect the creep behavior under strong winds although it is an elastic–plastic model 9 …”