Overall properties of particulate composites with fractal distribution of fibers

Abstract

Extensive research on the micromechanical structure of materials has revealed that some of the main construction materials exhibit fractal patterns at the micro scale. Therefore, micromechanical structure of these types of materials can be viewed as periodic structures at different length scales. A new homogenization technique is proposed that is mainly based on the micromechanical averaging schemes for the determination of the mechanical properties of materials with periodic microstructures. This method can be used in determining the overall properties of particulate composites. The proposed technique is a multi-step homogenization technique in which in each step a length scale is considered until the whole reinforcing phase is taken into account. To validate the method, its results are compared with the experimental data on different composite materials with different matrices and fibers. The results show that very good estimates of the mechanical properties is reached by utilizing the proposed multi-step homogenization technique. This method can be utilized in the determination of the mechanical properties of the composites with the coated fibers, where the effect of size of particles on the mechanical properties can be investigated by the application of principles of fractal geometry.