The　existing　constitutive　models　of　shape　memory　alloy　(SMA)　cannot　accurately　describe　the　mechanical　behavior　in　martensitic　strengthening　segment　since　their　loading　and　unloading　paths　in　strengthening　segment　completely　overlap.　This　study　proposes　a　multi-segment　linear　mathematical　model　for　SMA,　which　realizes　the　separation　of　loading　path　and　unloading　path　in　strengthening　segment.　A　four-story　steel　frame　structure　and　corresponding　braced　structures　with　various　SMA　constitutive　models　are　designed,　and　seismic　control　effects　of　SMA　braces　with　these　models　are　analyzed　and　compared　through　time　history　analysis.　The　results　show　that　the　sub-cycle　unloading　mode　of　SMA　constitutive　model　affects　the　seismic　mitigation　capacity　of　SMA　brace　in　a　certain　extent.　The　position　of　the　inflection　point　of　unloading　path　has　very　little　influence　on　the　structural　control　ability　of　SMA　braces.　The　SMA　brace　using　the　SMA　constitutive　model　with　a　single　linear　sub-cyclic　unloading　path　has　the　minimal　seismic　response　and　the　highest　seismic　reduction　ratio.　For　most　evaluation　indexes,　the　seismic　mitigation　ability　calculated　by　the　proposed　path　separation　constitutive　model　is　in　the　middle　of　the　results　calculated　by　the　existing　models.　SMA　models　without　considering　the　mechanical　behavior　of　strengthening　segment　may　lead　to　an　erroneous　estimation　of　the　energy　consumption　of　SMA　brace　and　the　structural　damage.　The　difference　of　simulation　results　among　various　SMA　constitutive　models　is　almost　independent　with　ground　motion.　©　The　Author(s)　2024.