Smeared Crack Approach and Fracture Localization in Concrete

The possibilities of the smeared crack concept for simulating crack propagation and fracture in concrete is investigated. A smeared crack formulation is proposed which treats concrete constitutive behaviour separately from crack interface behaviour. In this study concrete is in most cases modelled as having linearly elastic characteristics. For the crack (or the band of micro-cracks) tensile-softening and shear transfer are allowed to take place but no interaction between these phenomena is taken into account. A crack closing option is included. The model has been evaluated by using the DIANA finite element package. Three types of example problems are considered. First, mode I fracture in unreinforced concrete is discussed. Emphasis is placed upon the effect of the basic concrete softening properties, such as the shape of the strainsoftening branch and the value of the fracture energy Gr. The way in which stable and mesh-insensitive solutions can be obtained is demonstrated. Next, mixed-mode fracture in unreinforced concrete is discussed. Here, the predicted post-peak response is shown to be unstable, which has to do with the existence of a considerable number of cracks of which only a limited number is active while the majority is arrested or closed. Again mesh-sensitivity of the results is examined, not only with respect to mesh refinements but also with respect to a change in the orientation of mesh lines. Very fine meshes seem to be most promising for reproducing curvilinear crack trajectories. Finally, mixed-mode fracture in two shear-critical reinforced beams is analysed, one of which fails in diagonal tension and one in shear-compression. Sudden extensive diagonal cracking is shown to be simulated quite correctly, although it should be added that corresponding genuine limit loads are not always attained. Further, comments are made on the crack shear representation adopted, involving a constant shear retention factor. The principal outcome of the project is that pronounced fracture localization can in principle be predicted by using a smeared crack strategy. However, problems are also encountered to which no definite answers can yet be given. Throughout the article possible future approaches are indicated which may help to solve them.