Interpretation of the Griffith Instability as a Bifurcation of the Global Equilibrium

The process zone at the crack tip of a concrete-like material can be simulated in two different alternative ways: (a) with a damage zone in front of the stress-free crack tip, or (b) with a cohesive force distribution behind a fictitious crack tip. Both these numerical models are able to simulate the slow crack growth and to reproduce the scale effects of fracture toughness testing. With large structural sizes the softening structural behaviour disappears and the global ductility drastically decreases. In the damage model, this is due to the priority of the crack instability over the traditional structural instability. On the other hand, in the cohesive model, this is revealed by a bifurcation of the global equilibrium, the stress-singularity being not included in such a model.

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