A physically consistent virtual crack closure technique accounting for contact and interpenetration

In some circumstances, the standard formulation of the virtual crack closure technique (VCCT) may yield negative values of the modal contributions to the energy release rate. To avoid such physically meaningless results, a revised formulation is available. However, the revised VCCT does not take into account possible interpenetration of the crack faces, that may be predicted by the linearly elastic solution. The present work extends the revised VCCT formulation by introducing suitable contact constraints to prevent local interpenetration of the crack-tip nodes. By considering open vs. interpenetrated cracks and tensile vs. compressive crack-tip forces, four cases emerge. For each case, a suitable two-step crack closure process is outlined with the two steps respectively corresponding to fracture modes II and I. The contact pressure force, if present, is evaluated and accounted for in the computation of the crack closure work. As a result, novel analytical expressions are derived for the modal contributions to the energy release rate accounting for contact and prevented interpenetration.