ABSTRACT
Fracture properties of concrete are hard to separate from their structural environment. This is in short the message conveyed in the previous chapters. In Chapter 10, with the four-stage fracture model, the in¸uence of the structural boundary conditions and the geometry (shape and size) of the considered structure are incorporated via the geometrical factor, known from classical LEFM. Estimates for the size of the critical crack that leads to softening must be determined by means of an alternative model, for instance, the lattice model. Doing so seems unavoidable. The cohesive crack models will not work for concrete because the size of the cohesive zone is larger than the considered structure, and the original “local” plastic crack-tip model is changed into a “global” approach. It is quite essential that the structural component is included in the formulation. The 4-stage fracture model is an approach that might work. At the same time it should be mentioned that estimates for the geometrical factors are not always available, and it generally requires quite some effort to carry out the required analyses or experiments. Another approach that may be used is to return to a different form of lattice, which we refer to as “structural lattice.” The equivalence between lattice and particle models can be used conveniently in developing this new approach. Again, as in the last chapter, the material presented here has not yet led to a fully operational model. Of importance is developing the framework of the model ªrst, and showing its potential. Again, as in the 4-stage fracture model, the multiscale approach presented here is a good guideline for new experiments. After all, new insights are usually derived from carefully conducted and original experiments. Our modeling efforts are needed to summarize our knowledge in a uniform framework. The resulting model is no more than an approximation of physical reality. A critical assessment of the limitations and shortcoming of any modeling approach is therefore considered of the utmost importance.
