Thebridgedcrackmodelforreinforcedconcreteelementswithanonlinearmatrix

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 deY;ends on 1 three dimensionless parameters: w c E, which controls the extension of the process zone, N/ ) andN/~. called brittleness numbers, which are related to the reinforcement phases. The role of the specimen size scale is fun- damental 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 pa- rameters fixed and varying only the specimen size. · l INTRODUCTION tension of the model proposed by Carpinteri ( 1984) and by Bosco and Carpinteri (1995) for a discontinu- In the last few years, growing attention for cementi- ous fiber distribution and by Carpinteri and MassabO tious-matrix composite materials has been evidenced, (l 997a) for a continuous one. The longitudinal rein- in relation to the use of high-strength concretes. A pri- forcements are simulated by the actions of m concen- marily incentive in using fibers is to cut production trated forces directly applied onto the crack faces. The costs by reducing, where possible, the cross-section nonlinearities of the matrix are modelled by the action of the element or eliminating some forms of conven- of a continuous closing traction distribution onto the tional reinforcement.