Size effects on flexural response of reinforced concrete elements with a nonlinear matrix

A dimensionless formulation of the bridged and of the cohesive crack model 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. The peculiarity of the models consists in the imposition of both the equilibrium and the compatibility conditions to the cracked element. The constitutive flexural response depends on three dimensionless parameters: wc, which controls the extension of the process zone, N(1)P and N(2)P, related to the reinforcement phases. Eventually, some experimental and numerical examples are presented and discussed in order to validate the consistence of the proposed approach.