Shear behaviour of r.c. structures analyzed by means of two-parameters damage model

A local isotropic two-parameter scalar model able to simulate the mechanical behavior 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 addressed. The damage parameters are obtained directly from the value of two equivalent elastic undamaged stresses in order to reduce the computational effort. Due to the two damage parameters, this model is suitable for the study of both static and dynamic problems, involving arbitrarily variable loads. 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. This new feature assures 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 made on reinforced concrete beams, with or without shear reinforcement, failing in shear, have been carried out. The main results from the numerical analyses are described and compared with the experimental ones to demonstrate the effectiveness of the numerical method.