The bridged crack model for reinforced concrete elements with a nonlinear matrix

A Fracture Mechanics method for reproducing the constitutive flexural response of a reinforced concrete element with a nonlinear matrix is proposed. The nonlinearity of the matrix is modelled by considering a distribution of closing forces onto the crack faces which increases the fracture toughness of the cross-section with a shielding action. In order to take into account these closing forces, a dimensionless formulation of the bridged crack model is proposed, as well as its cohesive version. The constitutive flexural response depends on three dimensionless parameters: (w) over bar (E)(c), which controls the extension of the process zone, Np((1)) and Np((2)), called brittleness numbers, which are related to the reinforcement phases. The role of the specimen size scale is fundamental for the global structural behaviour, which can range from ductile to brittle simply with the variation of the two brittleness numbers. The numerical curves for such a case are presented, with all the mechanical parameters fixed and varying only the specimen size.