Size-effects induced bifurcation phenomena during multiple cohesive crack propagation

The non linear behaviour of concrete-like materials in tension is characterized by strain-softening. Phenomena involving the localisation of strain caused by strain softening can be analysed accurately through the so-called "cohesive crack model" which uses the length of the fictitious crack as a control variable. In this approach, the length of the process zone is not fixed and the ratio between this length and the length of the specimen decreases with increasing size-scale. This phenomenon is evident even for small changes in size. It can explain why, in four point shear test, a critical size is observed below which a secondary crack starts to propagate. This is a size-related phenomenon of bifurcation of equilibrium path, which is predicted by the cohesive crack model and confirmed experimentally. The theoretical results obtained by means of the cohesive crack model involving two cracks are in good agreement with experimental results.