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Large-rupture strain (usually larger than 5%) fiber-reinforced polymer (LRS FRP) composites are attractive materials for the seismic retrofit of concrete structures. Jacketing LRS FRP on concrete columns can effectively improve the ultimate strength and deformation of a concrete structure and make the concrete structure have excellent ductility and superior energy absorption capacity . In comparison with conventional FRP, the concrete under LRS FRP confinement experiences a more severe damage process when it is under large deformation . The confining pressure at the large deformation can alter the concrete plastic flow and significantly affect the cyclic stress-strain path of LRS-FRP confined concrete. This study evaluates the performance of existing cyclic models (e.g., unloading path, reloading path, and plastic strain) using a database including both traditional and LRS FRP-confined concrete. Through an analytical study on the cyclic response of LRS FRP-confined concrete, two key parameters (plastic strain and stress degradation) were found to significantly influence the cyclic behavior of LRS FRP-confined concrete. By defining these two critical parameters, a new cyclic stress-strain model was developed for LRS FRP confined-concrete with good performance. The proposed cyclic model was also applicable in predicting both post-peak strain hardening and softening behavior when used in a stiffness-based envelope model.