A novel restoring force model for metallic dampers incorporating performance degradation

Abstract

The metallic dampers have been widely used in energy dissipation systems. To more accurately describe their nonlinear mechanical behaviour, this paper develops a novel restoring force model incorporating performance degradation and complied into a UMAT subroutine with ABAQUS as platform. The force-deformation relationship of the proposed model is divided into two stages: small and large deformation stages. In the small deformation stage, the combined hardening model in the form of exponential functions is utilized to predict the restoring force of the dampers. Kinematic and isotropic hardening variables are introduced to reflect the Bauschinger effect and cyclic hardening of the metallic dampers, respectively. When the accumulative plastic deformation surpasses a specific value, the restoring force model transitions to the large deformation stage. In this stage, exponential function and sigmoid function are applied to modify the combined hardening model, reflecting stiffness and strength degradation caused by significant out-of-plane deformation and fracture of metallic dampers, respectively. To validate the accuracy and enhancement of the proposed model, experimental results from ten metallic dampers reported in the literature are compared with the simulation results of the proposed model and other three widely-used models. Three indices, in terms of the peak force $F_p$, the residual force at the final loading cycle $F_r$, and cumulative dissipated energy $E_a$, are employed to quantitatively evaluate the accuracy of the restoring force model. The results indicate that the proposed model accurately captures the mechanical behaviour of metallic dampers, with relative differences in these indices below 10 %. In contrast, differences between experimental results and the three other models typically exceed 10 %. Notably, since performance degradation is not accounted for in these three models, they overestimate the peak and residual forces of metallic dampers, with maximum errors reaching 30 % and 150 %, respectively. Additionally, the effectiveness of the proposed model under real-world conditions is verified by comparing results from Y-eccentrically braced composite frame specimens subjected to lateral cyclic loading and shake table testing. Finally, the limitations of the proposed model are also discussed.