An analytical approach of the fictitious crack model for concrete

Equations based on the fictitious crack model (FCM) for a mode I crack in concrete are developed. Once the material properties—the strain softening diagram—are evaluated through experiments, the length of the fracture process zone, the fracture stress and the stress distribution ahead of the crack tip corresponding to a preformed crack at the critical state of crack growth can be solved analytically. In this way, the computational efforts associated with the application of the FCM for analysing the crack formation and propagation in concrete can be greatly reduced. The above factors stimulate the implementation of the FCM in solving practical engineering problems. Typical examples are included and variations of the length of process zone, the fracture stress and the equivalent fracture toughness with respect to the preformed crack length are thoroughly studied.