Elastic properties of three-phase composites: analytical model based on the modified shear-lag model and the method of cells

A new general model to calculate the elastic properties of three-phase composites by means of closed-form analytical solutions is presented. The model is based on a combination of the modified shear-lag model and the method of cells. It does not require detailed knowledge of the microstructure. This confers the new model several advantages over previous methodologies, and makes it able to be used to estimate elastic properties of three-phase composites having very different matrix-reinforcements configurations, including anisotropy effect by introducing the fibre aspect ratio. The versatility and accuracy of the model have been tested on several different materials, including concrete mixtures, ceramics, metallic alloys, and natural rocks. Good agreement is found between the estimated effective Young’s modulus and the experimental results from the literature.