A novel mixed-mode cohesive law derived from a potential function is presented. The potential function is formulated using physical parameters that can be extracted from any fracture mechanics test capable of providing R-curves in terms of the J-integral as a function of the normal and tangential end-openings. The proposed cohesive law is able to describe the fracture behaviour of composites with large fracture process zones, including fibre bridging. As such, it is capable of describing both the crack tip, as well as the bridging region. An important aspect of the formulation is that the shape of the mixed-mode cohesive laws are derived and not assumed. The mixed-mode cohesive law was tested using synthetic data emulating mixed-mode fracture mechanics tests. The cohesive tractions extracted from the method exhibited characteristics which were not seeded on the model such as negative normal tractions under pure mode shear loading and non-zero shear loading under pure normal mode loading. •A novel procedure is proposed to extract mixed-mode cohesive laws from experimental R-curves.•Mixed-mode cohesive tractions are derived using a potential function defined in terms of the natural coordinate system of current fracture mechanics tests.•The derived mixed-mode cohesive laws accounts for both the crack tip and bridging tractions regions.•The derived cohesive laws are coupled in agreement with previous findings.