A prosthesis includes a tubular body of a graft material, a plurality of stents coupled to the tubular body, and a coupling. The coupling has a plurality of overlapping leaflets successively coupled to the tubular body around an opening formed in the graft material. The leaflets in a non-deployed configuration lay flush with the graft material of the tubular body and partially cover the opening, and the leaflets in a deployed configuration extend radially outward from the graft material of the tubular body. Delivery and deployment of a branch vessel prosthesis through the opening causes the leaflets to transform from the non-deployed configuration to the deployed configuration, and causes a diameter or width of a passageway defined by the leaflets to increase. Leaflet material properties, as well as size, shape, and sewing patterns on adjacent leaflets may be varied in order to vary the flexibility and/or orientation of the coupling.
