Path dependence of truss-like mixed mode cohesive laws

A general theoretical analysis is presented to prove that, under mixed mode fracture, truss-like mixed mode cohesive laws (cohesive laws that are coupled in a special manner such that the traction vector follows the separation/opening vector) are path independent only in the limited case where the fracture resistance (and effective traction) is independent of the phase angle of openings. To verify the theoretical analysis, a specific class of truss-like cohesive laws, coupled with a failure criterion for damage initiation and an effective opening displacement is used. It is shown analytically and numerically that these cohesive laws are path dependent.