Fracture Mechanics of Reinforced Concrete

The propagation of an element-wide blunt smeared crack band in a finite element mesh is analyzed. The results strongly depend on element size; e.g., a four times reduction in element size causes a 3.5 times reduction in the load to cause further crack propagation in a reinforced concrete planel. An energy criterion for crack band extension in concrete with a dense regular reinforcing grid is formulated and it is shown to be objective, i.e., the results for greatly different element sizes cioncide. This is achieved, however, only if bound slip near the crack band is also taken into account. An approximate formula for the lenght of bond slip of the bars crossing the crack band is derived, and for implementation in finite element programs an expression for an equivalent lenght of free bond slip (slip without bond stresses) is determined. The energy criterion is also generalized for nonlinear material behavior numerical results are given.