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This study presents a finite element model for a hybrid self-centering damper considering the rate and temperature effects and explores the effects of different design parameters on the damper response. The damper, called as superelastic friction damper (SFD), consists of superelastic shape memory alloy (SMA) cables and a frictional energy dissipation mechanism. The experimental response of the SMA cables, frictional unit and overall damper at different loading frequencies and temperature are used to develop numerical model of the damper. Once a validated numerical model is obtained, parametric studies are carried out to evaluate force-displacement response of the damper when the design parameters are altered. The effects of damper design parameters on the equivalent stiffness, dissipated energy, equivalent viscous damping and self-centering capabilities of the damper are analyzed. Based on the findings, the recommendations for the design of the damper are presented.