Microstructural based modelling of the elastic modulus of fiber reinforced cement composites

In this work, a new analytical model for predicting the elastic modulus of discontinuous fiber reinforced cement composites in uniaxial tension is presented. The proposed elastic modulus model depends on the macroscopic and microstructural parameters (interfacial bond modulus, matrix porosity, and so forth) of the composite. The microstructural scale is the fiber. The composite is considered to be a set of many fiber-matrix cells. The shear-lag concept is used to determine the forces and stress fields in the unit cell. The linkage between the microstructural and the macroscopic properties (homogenization) is made through an averaging process based on continuum mechanics, probabilistic considerations, and tensorial transformations. The model is applicable to all fiber orientations, probabilistic or deterministic. The particularities are that the model is triphasic and integrates the probabilistic density function of fiber orientation as a variable. Good agreement is observed between the model predictions and the limited experimental data available. The model is applicable to other discontinuous fiber reinforced quasibrittle matrix composites.