Continuous versus discontinuous bridged crack in the description of reinforced material flexural collapse

Two nonlinear bridged--crack models are formulated and proposed in order to explain and reproduce the constitutive flexural response of multiphase materials. The {\it{n--fibre discrete}} model applies to macrostructural studies of composites with brittle matrix and localized reinforcements or to microstructural analyses of fibrous composites. The {\it{continuous}} model applies to macrostructural analyses of brittle matrix composites with continuously distributed secondary phases such as fibre or particle reinforced materials. The two model formulations are briefly recalled and the resulting (moment versus rotation) constitutive relationships are explained and compared in the limit case of a composite with a high number of discontinuous reinforcements. The models both predict local discontinuities and a ductile--brittle transition in the global structural response when varying the mechanical and geometrical beam properties.