Localized fracture: Moot Point Computationally
First, we should recall that the cohesive crack model (i. e., the fictitious crack model of Hillerborg) and the crack band model yield about the same results (with differences of only about 1%, for h — hc) if the stress-displacement relation in the fictitious crack model and the stress-strain relation in the crack band model are calibrated through Eq. (8.3.1), that is, if the crack opening displacement w is taken as the fracturing strain that is accumulated over the width hc of the crack band. This equivalence, for example, follows from the fact that in the crack band model the results are almost insensitive to the choice of hc, as well as h, and in the limit for h – > 0 the crack band model becomes identical to the fictitious crack model (provided that the fracture energy equivalence is preserved, of course).
Thus, the question “Discrete crack or crack band?’’ is moot from the viewpoint of computational modeling. The only point worthy of debate is computational effectiveness and convenience. In the cases where boundary integral methods can be applied, the use of the cohesive crack model can be computationally more efficient. When the general finite clement method is used, these two models appear to be about equal when the fracture propagates along the mesh lines. However, the programming of the crack band model is generally easier, and that is why it lias been preferred in the industry. For other fracture paths, there are various differences but special methods must be used for both models.