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Recent works on finite element models for fracture and cracking of concrete are summarized and reviewed. An element-wide band of smeared cracks represents an effective and realistic model for fracture of plain concrete and reinforced concrete. The criterion for propagation of the band into the finite element in front of the crack band is expressed in terms of the energy consumed to create the cracks. It is shown that a tensile strength criterion, as currently used, is unobjective and gives incorrect convergence as the mesh is refined, with large differences between the results for finite elements of different sizes. However, it is possible to use an equivalent strength which depends on the element size in such a manner that the results are approximately the same as those obtained with the energy criterion. In the case of reinforced concrete, the forces transmitted between concrete and steel must be accounted for in the energy criterion. Furthermore, the bond slip of bars near the crack band must be taken into account, which may conveniently be done in terms of the equivalent free-slip length of steel bars.
fracture mechanics, concrete, rock, concrete structures, cracking, crack propagation, reinforced concrete, bond slip of steel in concrete, finite element methods, convergence, fracture criterion, fracture energy, ceramics, composite materials
Professor, Politecnico di Milano, Milan,
Professor of Civil Engineering and director, Center for Concrete and Geomaterials, Technological Institute, Northwestern University, Evanston, Ill.