Micromechanics modeling of cement concrete considering the interaction among randomly oriented ellipsoidal inhomogeneities

Abstract

To account for the random orientation of ellipsoidal inhomogeneities, the averaging process over two Euler angles has been widely used in existing micromechanics models. However, the interaction among various inhomogeneity orientations is often overlooked and may also affect the prediction of composite elastic modulus. In this work, to consider the interaction among randomly oriented aggregates and fibers in cement concrete, a micromechanics model, the orientation interaction model (OIM), is proposed. An orientation average model (OAM) is also proposed, and by comparing OIM and OAM predictions, the effect of inhomogeneity orientation interaction on the predicted elastic modulus is shown. In both models, geometries of coarse aggregates and fibers are approximated using ellipsoids with three different semiaxes and cylinders, respectively, and their orientations are described using three Euler angles. Compared with existing random orientation models using two Euler angles, the proposed models can capture the isotropy of composites with randomly oriented asymmetric ellipsoidal inhomogeneities. By comparing the predictions of OIM, OAM, composite sphere models and the Mori-Tanaka method with spherical inhomogeneities, it is found that with the increase of the stiffness contrast between the matrix and inhomogeneities, the effects of the inhomogeneity geometry and orientation interaction become more apparent. The model predictions agree well with the experimental data. By changing the value range of three Euler angles based on the inhomogeneity orientation distribution, both models are also suitable for transversely isotropic and anisotropic composites containing several types of inhomogeneities.