A fractal model of effective mechanical properties of porous composites

Abstract

In this work, a simple but effective fractal model is proposed to predict the mechanical properties of complex porous composites. By extending the Mori-Tanaka and Double Inclusion models, we develop a computationally efficient algorithm based on the mean-field homogenization, to quickly determine the macroscopic elastic properties of the random porous media by the fractal theory. The random pore sizes and locations are properly characterized by a single fractal dimension, and the fractal model agrees well with the numerical results obtained by the finite element homogenization technique and the existing experimental data from literature. Moreover, the effect of pore size distribution has been investigated, indicating that the elastic properties decrease with the increase in the fractal dimension. In particular, the computation time can be reduced from 4 h for the finite element analysis to 15 s based on the fractal model. Based on the mathematically analogous governing equations, the present fractal modeling has great potential to determine the other significant physical properties such as thermal conductivity and coefficient of thermal expansion.