Traction-separation relations due to large scale bridging in composites are very important in modeling their fracture response. Several works demonstrated that such relations are dependent upon the specimen's stiffness and loading conditions. Experimental data and micromechanics of bridging suggested that, in addition to the crack opening displacement (COD), the local curvature can be used as an additional kinematic parameter to incorporate the stiffness dependence on traction-separation-angle relations. In this work, analysis of data from DCB specimens with different stiffness, in three different materials, subjected to monotonic end opening forces, demonstrates that when the tractions are correlated with the product of local angle and COD, a stiffness independent traction-separation-angle relation is obtained, and can be implemented in an FE scheme. The methodology is further exemplified by fatigue data and fracture under pure moments that highlight the importance of the second kinematic parameter and the soundness of the approach.