**6. Conclusions**

A novel type of self-centering brace, namely the self-centering SMA-viscoelastic hybrid brace (SCVEB), was proposed in this study. The energy dissipation was provided by the SMA cables, as well as the viscoelastic dampers (VEDs), whilst the self-centering capacity was provided by the former. The fundamental mechanical behavior of individual SMA cables and viscoelastic dampers was first investigated, followed by a more comprehensive experimental study on a proof-of-concept SCVEB specimen. The main findings and conclusions are summarized as follows:

(1) The SMA cable exhibits typical flag-shaped hysteretic loops with a large recovery strain. Reasonable cyclic pre-training is suggested before anchoring to SCVEB, since this process was shown to help stabilize the hysteretic response.

(2) The VED is capable of providing reliable energy dissipation. The rubber in the test did not show rate-dependence property, such as typical viscoelastic material, and this may be due to the differences in their compositions.

(3) The SCVEB specimen exhibited satisfactory self-centering and energy-dissipation capability, although a certain degree of residual strain was observed due to manufacturing error. The participation of viscoelastic material, indeed, enhanced the energy-dissipation capability.

(4) The system-level analysis shows that the frames employing the proposed SCVEB have satisfied peak inter-story drifts under the MCE and almost negligible residual interstory drifts. More importantly, the SCVEB can further reduce the peak floor acceleration of the frames. These encouraging findings demonstrate that the proposed SCVEB could be a cost-effective self-centering solution by reducing member size of the boundary frame with less SMA consumption.

**Author Contributions:** Conceptualization, Z.-X.Z., Y.P. and X.H.; methodology, Y.P.; software, Y.P.; validation, Z.-X.Z., Y.P. and X.H.; formal analysis, Y.P., X.H. and Z.-X.Z.; investigation, Y.P.; resources, Y.P. and Z.-X.Z.; data curation, Y.P.; writing—original draft preparation, Z.-X.Z., X.H. and Y.P.; writing—review and editing, Z.-X.Z. and Y.P.; visualization, Z.-X.Z.; supervision, Y.P., X.H. and Z.-X.Z.; project administration, Y.P.; funding acquisition, Z.-X.Z. and Y.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** The financial supports from the National Natural Science Foundation of China (NSFC) with Grant Nos. 52078359 and 51778456 are gratefully acknowledged. Support for this study was also provided by the Shanghai Rising-Star Program (20QA1409400).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data presented in this study are available in this article.

**Acknowledgments:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

