Finite element modeling of crack band propagation

The propagation of blunt smeared crack bands through a finite element mesh in plain or reinforced concrete. structures is studied. A previous work, which demonstrated (approximate) independence of results from the chosen mesh size, is extended by demonstrating the same for the changes in mesh orientation with regard to the crack band and to the steel bars. Bond slip of bars must also be considered. This is satisfactorily accomplished by extending the previously proposed concept of free bond slip length for the cases of skew meshes and skew bars. In the presence of reinforcement, the previous formula for the equivalent strength giving approximately the same results as the energy criterion must be expanded by a term which corresponds to the third term of the asymptotic expansion of displacements near the tip of a sharp crack. The energy criterion is shown to give consistent results for different types of fracture specimens. However, the equivalent strength calibrated for the center-cracked tensile specimen leads to a greater error (about 15%) when applied to bent specimens. Thus, the similar equivalent strength approach is acceptable only if fine meshes are used although correct convergence appears to occur as the mesh size tends to zero.