Cyclic behavior and seismic control performance of SMA friction damper

Using superelastic shape memory alloy (SMA) bars and non-asbestos organic friction material, this study developed an innovative self-centering friction damper (SCFD). This hybrid passive control device consists of the self-centering device using SMA bars and the friction energy dissipation device which can provide excellent self-centering ability and energy-absorbing ability to meet the requirements of civil engineering applications. To explore the feasibility and hysteretic properties of the SCFD, experimental tests under cyclic loading were conducted. According to the experimental results, the proposed SCFD exhibited a stable and repeatable flag-shaped hysteretic response, which can achieve the recovered displacement of 76.07% and dissipated energy of 6.04 kJ at 42 mm. The finite element model of the SCFD using ABAQUS software was established and validated by experimental results. And a series of numerical simulations with different parameters were performed, which enables a more in-depth interpretation of the SCFD. Additionally, a system-level nonlinear time-history analysis was performed on a three-story steel frame equipped with and without SCFDs. The dynamic analysis results indicated that the SCFDs could effectively reduce structural damage and enhance post-earthquake recoverability under rare earthquakes.


Introduction
Structural vibration control techniques, including active and passive controls, control the structural response under an earthquake to ensure the safety and serviceability of the building, thereby increasing the occupancy comfort and minimizing the loss of building content [1][2][3]. In civil engineering, the most widely used vibration control strategy is passive control because of its reliable control efficacy and * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. cost-effectiveness [4,5]. However, the recent commonly used passive devices such as friction and metallic dampers do not exhibit self-centering characteristics, which implies that unrecovered post-earthquake residual deformation may exist in structures, and this significantly influences the functionality of the structure [6][7][8]. As a critical index, residual deformation can more comprehensively characterize the resilience performance of a structure and potential damage that system has suffered after an earthquake. As reported, structures with residual inter-story drift ratio (RIDR) higher than 0.5% are more economically advantageous for demolishing buildings than repairing them [9], whereas those higher than 1.0% are typically demolished [10]. Considering this situation, selfcentering dampers have developed rapidly over the past few years, devoting damping to the capability to reduce postearthquake residual deformation [11][12][13][14].
Conventional passive energy dissipation devices, such as metal, friction, viscoelastic, magnetorheological dampers, and buckling-restrained braces, may exhibit residual deformation after the earthquake, which requires replacement with new devices. Recently, shape memory alloy (SMA)-based self-centering structures have become the subject of increasing interest and research efforts. Owing to their advantageous properties of fatigue resistance, good damping behavior, excellent corrosion resistance, and remarkable superelasticity [15,16 ], various researchers have used SMAs for the seismic control and have verified their effectiveness in designs and applications, such as passive dampers and beam-to-column connections [17][18][19][20][21]. Li et al [18] proposed a new damper based on SMA wires and performed a nonlinear time-history analysis on a six-story steel frame with SMA dampers. Wang et al [22] conducted a comprehensive study on the mechanical performance of large SMA bars and proposed self-centering beam-to-column connections by combining SMA bolts and steel angles. Additionally, Savi et al [23] and Fang et al [24] and Wang et al [25] validated the excellent performance of SMA as helical springs, Belleville springs, and ring springs by conducting a series of experimental tests and numerical analyses.
Although almost all extant studies successfully demonstrate the self-centering capability of SMA-based dampers under cyclic loading, it is noteworthy that their energy dissipation capacity is relatively limited. Therefore, hybrid dampers that combine SMAs and energy dissipation devices have been designed to realize higher seismic control effectiveness. Qiu et al [17] proposed an SMA-steel damper that combined SMA elements with steel dampers. Zhang et al [26] developed a novel deformation-amplified damping system by combining a lever arm amplifying mechanism and a friction-adjusting device. Experimental and numerical studies were performed, and the results indicated that this novel damper exhibits excellent control effectiveness compared to other dampers. Gur et al [27] attempted to improve the compliant liquid column damper by replacing the linear spring with a nonlinear flexible spring made of SMA. By conducting a series of parametric studies, the enhanced performance of this new damper over a conventional compliant LCD was demonstrated. Furthermore, Liu et al [28] proposed an innovative self-centering negativestiffness damper combining SMA and prepressed springs to enhance the damping performance by introducing negative stiffness. The numerical simulation results indicate that the damper can achieve a larger damping ratio owing to the effect of the negative stiffness, and the acceleration and displacement response of the SDOF system can be reduced remarkably.
However, among the above-mentioned SMA-based devices, some critical issues need to be addressed. For example, BRB and metallic yielding dampers tend to exhibit asymmetrical cyclic behavior, and the stiffness and strength of them decrease sharply after an earthquake [12,17]. In this case, the friction device appears to be a potential choice for increasing the damping of SMA-based dampers. Gao and Ren [29] proposed an innovative SMA-friction damper which consisted of SMA wires and friction sheets. By combing pretensioned SMA wires and a friction device, Qian et al [30] developed a new SMA friction damper and shaking table tests were conducted to demonstrate its effective in suppressing the dynamic response of the building. Lu et al [31] conducted a series of experimental and numerical studies to investigate the hysteretic behavior of a novel SMA-friction damper. Qiu et al [32] designed a new SMA slip-friction damper and the cyclic behavior of a steel self-centering rocking column with a pair of new dampers was investigated.
Some advantages of friction devices are [33]: (i) stable energy dissipation capacity; (ii) independence between the energy dissipation and the amplitude, frequency, and number of cycles of the input; (iii) high resistance to fatigue; (iv) stable behavior at different temperatures; and (v) repeatable behavior and manufacturing simplicity. Therefore, in this study, friction devices were adopted as the energy dissipation elements in a self-centering damper, where the friction force is generated between the 65Mn material and non-asbestos organic (NAO) plates.
In this study, an innovative self-centering damper was proposed to enhance the self-centering capability and dissipating energy, and its cyclic behavior was evaluated experimentally and numerically. Cyclic tests of the fabricated damper were conducted, and a series of numerical simulations were performed using the ABAQUS software. Furthermore, to demonstrate the effectiveness of the proposed damper in structural seismic control, a system-level nonlinear time-history analysis was performed under three seismic excitation intensities.

Self-centering friction damper
The self-centering friction damper (SCFD) consists of a selfcentering device and friction device, as shown in figure 1. The self-centering device was composed of an inner steel plate, outer steel plate, dam board, push-pull board, and SMA bars. The friction device consists of friction plates, friction restraint plates, and NAO plates. The NAO material was selected for the frictional energy dissipation device of the damper because of its light weight, good abrasion resistance at low temperatures (less than 200 • C), and excellent durability with stable energy dissipation capacity; these properties can enhance the applicability of energy dissipation devices [34,35].
The SCFD is hinged to structural components, facilitating its installation and replacement. As shown in figure 2, the working principle of the SCFD is introduced [36]. The SMA bars are placed parallel to the loading direction of the SCFD and are forced to elongate when the SCFD is loaded under either tension or compression. Initially, the pair of push-pull boards is in contact with the corresponding dam board. When the SCFD is subjected to a tensile (compressive) load equal to the sum of the frictional force and the strength of the SMA bars, the middle steel plate pushes the right (left) push-pull board to elongate the SMA bars. The maximum distance is the length of the groove in the middle steel plate, which can be designed to achieve the best superelastic effect of the SMA  bars. The SMA bars and friction plates work together to dissipate energy, and after unloading, the self-centering device restores the SCFD to its original state.

Specimen details
A large-scale SCFD of 1310 mm was designed and fabricated based on the optimal results of a previous study [36]. The critical dimensions of the fabricated specimens are shown in figure 3. SMA bars with a composition of 55.9%Ni-44.1%Ti were provided by Baoji Haipeng Metal Material Co., Ltd. The martensite finish temperature M f is −40 • C, the martensite start temperature M s is −25 • C, the austenite finish temperature A f is 5 • C. Four SMA bars with a length of 750 mm and a diameter of 9 mm were used in the damper. Using a wedge and barrel anchorage to fix the SMA bars, an effective length of 600 mm was obtained. Based on the optimal results in previous studies [36,37], the relationships between the total cross-sectional area of the SMA bars (A) and the friction force (f ) were established, i.e. f = 0.100 A. Thus, the friction force is calculated as 25.45 kN given that the cross-sectional area of SMA bars is 254. 47  NAO plates with a thickness of 5 mm, width of 60 mm, and length of 120 mm were embedded into the friction plate. The friction provided by NAO material could be calculated as follows: where n f is number of friction surfaces. µ f is the friction coefficient between NAO and 65Mn steel, which is 0.4. P is the pre-tightening force of the bolt group. During the experiment, by applying torque to the bolts, the shaft pressure is transferred to the friction plate to apply friction force. The torque T can be calculated as follows: where K is torque coefficient, and for general condition with no lubrication, the value is 0.2. d is the bolt diameter.

Test setup and loading procedure
The tests were conducted using a servo-hydraulic actuator (POPWIL MAS-1000 kN) with a maximum capacity of 300 mm (±150 mm) displacement at the Construction Structure & Earthquake Resistance Lab of Chang'an University. The SCFD was oriented vertically, as shown in figure 4, where the top and bottom ends were connected to the actuator and strong floor beam, respectively. Both ends of the SCFD were pinned using rigid connecting plates with pin shafts. This boundary condition is typical for dampers used in practice because it ideally induces no secondary bending [38,39]. Force and displacement were automatically recorded by sensors embedded in the actuator during the test process.
The loading procedure started from ±6 mm displacements to ±42 mm with an incremental interval of 6 mm, corresponding to 1%-7% strain in the SMA bars. The load was applied quasi-statically at a loading rate of 0.9 mm s −1 , and two repeated cycles were applied for each displacement amplitude.
The temperature during the tests was around 25 • C. The SMA bars were trained before the formal test to obtain admirable properties, which included two steps: first, the SMA bars were heated at 400 • C for 30 min, followed by water quenching, and second, the SMA bars were subjected to 20 loading cycles at a strain amplitude of 3% at 0.005 Hz.

Experimental results
The reliable hysteretic performance of self-centering and friction devices is the premise of generating the desirable behavior of the SCFD. Hence, the self-centering and friction devices were tested individually prior to the test on the SCFD. In the first stage, only friction device was assembled. The normal pressure applied to the friction plate is controlled by adjusting the torque applied to the bolts, thus, the output friction force can be obtained. The precise friction force is achieved through small adjustments to the bolts torque. In the second stage, four SMA bars were installed into the SCFD and anchored, while the bolts on the friction plate were loosened so that the friction force was set to zero, allowing the self-centering device to be tested separately.
As shown in figure 5(a), the friction device provided a stable value of force without obvious degradation. The force  generated by friction device is 25.26 kN. After loading tests, there no crack but only few slight scratches on the NAO plates, which is resulted from friction mechanism. The self-centering device had steady hysteretic loops that exhibited symmetrical double-flag hysteretic behavior. The force generated by friction device is 25.26 kN. Note that although the test curves are slightly asymmetrical about the coordinate origin, the minor clearance between components by manufacturing tolerance that arises when the SCFD is subjected to various tensioncompression loading cycles introduces inevitable errors in the results.
The hysteretic curves of SCFD are shown in figure 5(b). The SCFD exhibits symmetrical behavior under tension and compression actions and exhibits excellent energy dissipation capacity and self-centering ability. As the amplitude of the displacement increased, the residual displacement increased slowly. The residual displacement in the hysteretic curve primarily includes three parts: (i) D r1 : the deformation caused by friction force. Based on the test data, D r1 = 3.97 mm, which is defined as the residual deformation at the first loading cycle; (ii) D r2 : the inevitable rigid body movement of the SCFD during the test resulting from the minor clearance between the friction plates and dam boards, which is related to manufacturing and fabrication. Its value becomes gradually stable with the loading process, as shown in figure 5(b), and D r2 = 2.50 mm can be obtained; (iii) D r3 : the residual strain of SMAs during the cyclic tests, which is associated with the completion of austenite to martensite phase transformation, and its value is 3.5 mm. Note that the hysteretic curve of the damper did not have an obvious yield point; the main reason for this phenomenon is as follows: The two ends of each SMA bar of the SCFD were fixed by strand tapered anchorage, and this configuration causes inevitable little drift when subjected to cyclic loading, resulting in non-synchronization of the deformation development of SMAs. Thus, the SMA bars failed to yield at the same displacement.
A more detailed illustration of SCFD performance is shown in figure 6. As the response is generally symmetrical, as shown in figure 5(b), the average values obtained from both loading directions, such as the peak force F max and residual displacement D r , were given for quantities. Figure 6(a) plots the generated peak force F max in the SCFD and the secant stiffness K. The F max reached 146.20 kN in the last loading loop. With increasing the displacement amplitude, the values increase but the increment slowed down as the result of the forward phase transformation of SMA bars. The K is calculated as the ratio of the peak force F max to the maximum displacement D max at that cycle. The value is around 10 kN mm −1 at the first two cycles and then decreases, and the changing degree matches that found in the F max . The value is stabilized at around 3.50 kN mm −1 at late loading stages, where the nonlinear force-displacement behavior is significant.
The calculated energy dissipation W and equivalent damping ratio ξ eq of the SMA damper for every cycle are shown in figure 6(b), where W denotes the area surrounded by a curve with one loading cycle. Evidently, W increases as the external displacement increases, and the degradation between the two cycles under the same displacement amplitude can be ignored. When the SCFD is fully tensioned, the maximum value of W achieves 6.04 kJ per loading cycle. ξ eq can be calculated as follows: where W E is the energy stored in a linear system undergoing the same maximum displacement. The values of ξ eq ranged between 15.39% and 17.40% and remained relatively stable throughout the entire process. It is interesting to note that the SCFD shows a high level of ξ eq from the beginning of the loading process, which is due to the friction-induced energy dissipation mechanism that is mobilized early. The stable ξ eq behavior implies that the SCFD could effectively contribute to the energy dissipation for structures at small inter-story drifts [39]. In particular, the maximum value of ξ eq reached 17.40% at an amplitude of 18 mm. ξ eq decreases afterward, which could be attributed to the more remarkable increase in W E , as shown in equation (3). Figure 6(c) shows that the residual deformation D r gradually accumulated with an increase in the displacement amplitude. The values exhibited an almost linear relationship with the displacement amplitude. Due to the inherent properties of SMAs, when subjected to incremental cyclic loading, the residual strain is gradually accumulated with an increase in the maximum strain. Besides, minor clearance between the SCFD components also causes some unrecoverable deformation. When the displacement amplitude was 42 mm, the value was 10.05 mm, indicating that over 76.07% of the displacement was recovered.

Modeling approach
To further investigate the performance of SCFD, finite element (FE) simulations were conducted using the ABAQUS (version 2020) program. Compared with experimental research, numerical simulations are more economical and convenient, and details that are difficult to observe in loading tests, such as local deformation and stress distribution, can be revealed by FE models.
The ABAQUS superelastic material model was considered for the SMA bars, and the bilinear elastoplastic model was assigned for the steel components. All material properties used in FE modelling are the same as those discussed in section 3.1. For mesh creating, the C3D8 element was used for the SMA bars, and C3D8R element was used for the other steel components. To increase the simulation accuracy of the numerical results, the fine meshes were applied to the SMA bars, friction plates, whereas the relatively coarse meshes were applied to the other components to reduce computational cost, as shown in figure 7.
Both ends of the SCFD were constrained to a reference point with multi-point coupling constraint to produce a statically uniform displacement. The displacement was applied at one end, and the other end was fully fixed. Two loading time steps are considered. In the first step, the bolt loads were applied to complete the loading of friction force. Then, cyclic loading was applied to the inner steel plate to observe the force-displacement behavior of the model. The loading procedure was the same as that used in the tests and only one cycle was performed for each displacement amplitude.
Nine models were simulated, including the variations in the friction force and pretension of the SMA bars. The differences between all the cases are summarized in table 1. In three cases, the SMA bars were replaced with Q345 steel bars to investigate their effect of the SMA bars.

FE model validation
The hysteretic behavior for both numerical and experimental models are shown in figure 8. To quantify the simulation accuracy, two critical parameters were computed and assembled, as listed in table 2. It can be observed that the errors were within 10%. Note that a gradual accumulation of residual strain of SMAs when subjected to repeated loading was not considered in the ABAQUS built-in superelastic material model. Despite the discrepancy, figure 8 shows that the force-displacement behavior of the SCFD predicted by the simulation is reliable, especially for design purposes, because the predicted maximum force-displacement capacities match the experimental results. Therefore, further parameter analyses were performed using the established FE models.

Simulation results
As shown in figure 9(a), the larger the friction force, the larger is the area surrounded by the hysteretic curve, indicating that the energy dissipation has improved significantly. Moreover, by increasing the friction force from 25 kN to 40 kN, the maximum residual deformation is increased from 3.91 mm to 15.21 mm. Figure 8(b) shows three steel friction dampers. A large value of unrecoverable residual deformation can be observed, and the behavior of the FD is not symmetric. The energy dissipation of FDs increases with the increase of friction force. However, Q345 steel bars show little energy dissipation only in tension loading. When the damper is in compression loading, only the friction device is contributed to the energy dissipation. Because Q345 steel bars have no selfcentering ability and cannot restore to its original state after the tension loading, they have little effect on energy dissipation characteristics of damper when subjected to compression loading. Figure 9(c) shows the effect of varying the pretension of the SMA bars on the hysteretic behavior of the SCFD. Obviously, the SMA pretension can eliminate the residual deformation of SCFD. With the increase in pretension, the forward phase transformation occurs earlier. Therefore, the actual strain in SMA bars exceeded 7% when the displacement amplitude reached 42 mm, which should be considered from the designer's standpoint to design the maximum work displacement of the SCFD.

Performance evaluation
Three representative FE models, namely, SD-40, SD-P10, and FD-40, were selected for further evaluation. The stress      distributions are shown in figures 10 and 11. The stresses were localized at the working parts of the SCFD, such as SMA/Q345 steel bars, inner/outer steel plate, and push-pull board. There were small residual stresses in the bolts (approximately 50 MPa), as shown in figures 10(c) and 11(c), which were used to apply the friction force. Owing to the accumulation of unrecovered plastic deformation of the Q345 steel bars, FD-40 could not be returned to its original position after unloading. Figure 12(a) plots the stress-strain behavior of the SMA bars in the SD-40. Figure 12(b) shows the same diagrams for the SD-P10, and as the SMA bar pre-strain ε pre increased, the actual stress axis moved to the right direction. Figure 12(c) exhibits stresses and strains in a Q345 steel bar. The maximum   Evidently, the stiffness of loading and unloading was always close to the initial stiffness, and the plastic strain generated in the loading process would gradually accumulate. FR (force ratio), RR (recentering ratio), and ER (energy ratio) were selected to quantify the mechanical properties of all models, as suggested by Mirzai et al [40], and they are introduced as follows: where F SMA,re , F st,y and F fr,max refer to the self-centering force of the SMA bars, yielding force of the Q345 steel bars, and friction force, respectively. Where D max and D res refer to the maximum and residual displacement of the damper, respectively. E fr refer to the energy dissipations of the friction device, and TE is the total energy dissipation of the damper. The corresponding values are summarized in table 3. D SMA,res , D st,res , and D fr,res refer to the residual deformation of the SMA bars, Q345 steel bars and friction device, respectively. D res refers to the total residual deformation.
The energy dissipation decreases with a decreasing FR ratio. As shown in table 3, the FR ratio in SD-P10 was close to 100%, but it was minimal in the three FD models. The RR ratios for SD-P2.5, SD-P7.5, and SD-P10 were all greater than 95%, and the value shows the self-centering capability of the damper. However, it decreased from 90.69% to 63.79% when the friction force increases from 25 kN to 40 kN. In addition, the RR ratio was significantly improved after applying pretension to the SMA bars.
In all models, values of ER were higher than 100%, indicating that most of the energy was contributed to the friction device. TE defines the total cumulative energy. The maximum energy dissipation in table 3 was 33 296.19 kN • mm, which was related to SD-40. Moreover, the energy dissipation damped by the SMA bars was significantly higher than that of the Q345 steel bars.

Enhancing seismic performance of a steel frame
Although the previous sections of this study provide insight into the hysteretic characteristics of SCFD, further investigation is required to understand the behavior of structures incorporating SCFDs. In this section, SCFDs are installed into a three-story frame, and the seismic control effect are investigated by numerical simulations.

Overview of the structural modeling
A 3-story steel frame, designed by Song [41], was selected as the prototype structure. The frame elevations are shown in figure 13. The dimensions of the beams and columns were H250 × 200 × 8 × 14 and H200 × 200 × 8 × 12, respectively. The seismic mass is 2 × 10 4 kg at each level. Moreover, L90 × 90 × 12 double angles were used for the chevron brace configuration, and the SCFDs were placed horizontally. Q235 steel was applied to the columns and beams in the model, and all parts of the frame were modeled using C3D8I solid elements.
The working length of the SMA bars was determined such that when the controlled structure was designed with an allowed inter-story drift ratio (AIDR) of 2.0% [42], the corresponding strain sustained by the SMA bars reached 7% [26,43]. Thus, the length of SMA bars in the SCFDs was equal to 1200 mm, and the other parameters were the same as those of SCFD-25 in section 4.1.
Prior to the dynamic time-history analysis, a static pushpull analysis, employing a lateral force to the third story of the frame, was performed to understand several key system-level hysteretic characteristics of the prototype frames, as shown in figure 14. As anticipated, the frame with SCFDs shows bigger fat hysteretic loop than the uncontrolled frame, which is resulted from the excellent energy dissipation of SCFDs. When the push-pull displacement is less than 150 mm, the pinching effect in hysteretic loops of controlled frame is significant compared with the uncontrolled frame. The uncontrolled frame shows strength of 144.39 kN, while the controlled frame is 425.23 kN, indicating that the use of SCFDs increases the strength of the frame by 294.5%, and furthermore, the overall stiffness of the system is significantly improved. When the frame is deformed by seismic response, the SCFDs provided continuous support to the frame structures. The adequate loadresisting capability of the SCFDs effectively sustained the frame strength; prevented structural members from reaching higher drifts, and thus greatly enhanced the structure performance.
Three earthquake ground motions are selected herein as: El Centro, Taft and one artificial seismic wave, of which the time histories and spectra acceleration demands are shown in figure 15. The maximum duration of each earthquake ground motion was extended for 30 s by adding zero accelerations, which allowed the vibration to decay completely. Before the numerical simulations, the PGA of each earthquake ground motion is further scaled up to 0.2g, 0.4g, and 0.6g based on the Chinese code for seismic design of buildings, which are supposed to represent the design, rare, and extremely rare earthquakes, respectively. When the earthquake ground motion is input into the main frame, the corresponding seismic response produces deformation feedback for the SCFDs. Then, SCFDs generate a control force on the main frame and constrain the structural responses accordingly.

Structural seismic responses and discussions
The displacement response time history was plotted to demonstrate how the installed SCFDs affect the structural vibration mode in the time domain. Figure 16 shows the displacement time histories for each story under three earthquake ground motions (PGA = 0.6g). Obviously, the displacement amplitude of each story for the uncontrolled structure is clearly larger than that for the controlled structure, indicating that the seismic control effect is significant. The structure tends to vibrate around the initial position owing to the self-centering capability of the SCFDs.
Peak displacement (PD), peak inter-story drift ratio (PIDR), and RIDR are commonly considered as major parameters for assessing the seismic responses of buildings [44][45][46]. In this study, these three parameters were examined, and figure 17 shows the corresponding results. The elastic inter-story drift ratio and AIDR, as specified in the Chinese code for seismic design of buildings (0.4% and 2.0%), are plotted in figure 17 for comparison purposes. Furthermore, as for RIDRs, FEMA P-58 [47] defines four classes of IDR limits, where the first class, DS1, requires the RIDR to be less than 0.2%, such that 'no structural realignment is necessary for structural stability, but the building may require adjustment and repairs to nonstructural and mechanical components'. Therefore, DS1 is plotted in figure 17.
As shown in figure 17, the PDs for each story under the three earthquake intensities are efficiently controlled using    SCFDs. The PIDRs were attributed to the non-accumulation of deformation in the controlled structure, whereas the inelastic deformations of the uncontrolled structure accumulated during the seismic response. Specifically, under an El Centro extremely rare earthquake ground motion (PGA = 0.6g), the building collapses because the maximum PIDR exceeds the AIDR, as shown in figure 17(c). Smaller PIDRs were obtained when SCFDs were added to the structure, and the controlled structure did not collapse because all PIDRs were smaller than the AIDR.
For the RIDR response, the results show that the controlled and uncontrolled structures satisfy class DS1 under the design earthquake ground motion (PGA = 0.2g). For uncontrolled structures, however, rare and extremely rare earthquake ground motions of El Centro result in RIDR values that exceed 0.2% but are within 0.5%. Based on design guides [47], realignment of the structural frame and related structural repairs is economically feasible, and the degradation in structural stability is limited. When the SCFDs were installed, all RIDRs were below DS1. The structural responses are attenuated because more seismic energy is dissipated by the SCFD and less energy is transferred to the structure. Moreover, after earthquake excitation, the structure was driven to be self-centering by the restoring force of the SCFDs, resulting in a significant reduction in residual displacements.
To explicitly demonstrate the seismic control effectiveness, the reduction ratios were introduced as follows: The average reduction ratios of these three parameters under three earthquake ground motions are listed in table 4. The PDs, PIDRs, and RIDRs for each story under the three earthquake intensities were found to be efficiently controlled using SCFDs. In particular, the average reduction ratio of the PIDR for PGA = 0.2g is 74.44%, whereas for PGA = 0.6g, it is only 43.80%. This was probably due to the inadequate restoring force of the SCFDs. Evidently, the SCFDs provide a sharp decrease in the RIDRs in the structure, and the maximum reduction ratio was 97.94%. The results discussed above clearly demonstrate the positive role of SCFDs in reducing the PD, PIDR, and RIDR for steel frames.

Conclusions
This study presents a novel passive energy-dissipating device using superelastic SMA bars to achieve self-centering ability and friction material to enhance the energy-dissipating capacity. Experimental and numerical studies were conducted to explore the mechanical properties of the damper. Nonlinear time-history analysis was performed to study its effectiveness in controlling the structural vibrations. The notable conclusions are summarized as follows: (1) The experimental results confirmed the feasibility of this self-centering friction device, and the SMA self-centering part worked well with the friction device. The SCFD has stable flag-shaped hysteresis loops, which exhibit excellent energy dissipating capacity and self-centering ability.
(2) The energy dissipation increased as the external displacement increased, and the maximum value was 6.04 kJ.
Owing to the friction-induced energy dissipation mechanism, the SCFD shows a high level of equivalent damping ratio from the very beginning of the loading process, which implies that it could effectively contribute to energy dissipation for structures at small inter-story drifts. Residual deformation is inevitable owing to the friction mechanism, minor clearance, and SMAs, but when the applied displacement was 42 mm, the value was just 10.05 mm, indicating that 76.07% of the displacement was recovered. (3) The SCFD showed a symmetric behavior, whereas the damper using Q345 steel bars did not properly dissipate the energy in pressure owing to residual displacement. In addition, the stresses were primarily localized at the SMA bars when the SCFD was in the working condition, and the other parts of the damper were in the elastic range, which confirmed the reasonability of the damper design. The main components under the stress of the SCFD are the push-pull board and inner steel plate. (4) The friction device can effectively improve the energydissipation ability. However, the residual displacement increased significantly when the friction force increased to a certain extent. With increasing pretension of the SMA bars, the residual deformation decreased gradually, and the maximum dissipation energy decreased. (5) The system-level nonlinear time-history analysis confirmed that the SCFD could effectively reduce the PDs, PIDRs, and RIDRs. Specifically, the average reduction ratio of the PD for PGA = 0.2g is 66.79%, and the maximum reduction ratio of the RIDR is 97.94%. The maximum RIDR is reduced from over 0.2% to below 0.04% under extremely rare earthquakes, implying the superior performance of SCFDs for eliminating residual displacement.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).