Compliant joints have a number of advantages that make them suitable for highly constrained design problems. While much work has been done on the design of compliant joints manufactured from planar sheet materials, this work focuses on the design of cylindrically-curved joints. A method for using lamina emergent torsional (LET) joints to increase energy storage efficiency in curved sheet materials is presented. A numerical model is provided for predicting the stiffness and maximum applied moment of a curved LET joint. Predicted curved LET joint stiffnesses and maximum moments are utilized to create shape factors that produce an effective modulus of elasticity and an effective modulus of resilience. For a given case, the effective modulus of elasticity is shown to decrease by about three orders of magnitude while the effective resilience decreases by approximately one order of magnitude. Designers can use this information to tailor materials to fit design requirements or to select alternative materials that were previously unsuited for an application.