Energetically orthogonal fracture mode partitioning of the J-integral for cohesive interfaces

This work explains how the J-integral can be split into the sum of two physically consistent, positive definite, mode I and mode II contributions. To this aim, the concept of energetic orthogonality between fracture modes is exploited. More in detail, it is assumed that mode I is related to a null tangential relative displacement at the crack tip, Δt = 0, and that the forces related to mode II are energetically orthogonal to those related to mode I. The same concept has already been applied to partition fracture modes in finite element models by the virtual crack closure technique (VCCT) and in beam-theory models of laminated beams. Here, the method will be first illustrated with respect to linear, coupled cohesive laws and then extended to nonlinear, coupled cohesive laws.