A statistical micromechanical model of multiple cracking for ultra high toughness cementitious composites

A new statistical micromechanical model of multiple cracking is proposed in which a general expression of the fiber bridging stress laws in the crack plane is established. In this model, the random distribution properties of fibers are considered. And the Weibull function is adopted to represent the flaw size distribution. The relationships of stress versus strain and crack width versus strain are proposed. The formulas of the crack width, crack space, strain capacity and fracture energy density at the end of multiple cracking processes are also deduced. The validity of the proposed model was demonstrated by experimental results.