A scalar damage model with a shear retention factor for the analysis of reinforced concrete structures: theory and validation

A local isotropic single parameter scalar model that can simulate the mechanical behaviour of quasi-brittle materials, such as concrete, is described. The constitutive law needs the mechanical characteristics and the fracture energy of concrete to be completely defined. The damage parameter is obtained directly from the value of an equivalent effective stress in order to reduce the computing effort. Due to the unique damage parameter, this model is suitable for the study of quasi-static problems involving monotonically increasing loads. The problem of localisation and mesh dependency have been partially overcome by using an enhanced local method in which a characteristic internal length related to the mesh dimension is employed instead of the characteristic fracture length. In this work, the model was enriched further with the introduction of a shear retention factor that accounts for the friction between the two surfaces of a crack. These new features assure a real improvement of the damage model, maintaining nevertheless its simplicity and low computing cost and making it suitable for the practical solution of large scale problems. Several numerical simulations of experimental tests, concerning fracture tests on concrete specimens and beams failing in shear, have been performed for the validation of the model. The main results from the numerical analyses are described and compared with the experimental ones.