A study on homogenization equations of fractal porous media

Abstract

Fractal dimension can effectively describe the microstructure of self-similar fractal porous media, and it is of great significance to predict their macroscopic mechanical properties by different fractal dimensions. Based on fractal theory and the Mori-Tanaka method, homogenization equations of fractal porous media were deduced by tensors in this paper, and the parameters affecting the prediction results and the macro mechanical properties were discussed. The numerical results show that the homogenization equations are reliable, and the value of λ f,min/λ f,max has an influence on prediction results and the macro mechanical properties. When the pore fractal dimension is close to 1.4, the prediction results by fractal homogenization equations in this paper are more accurate. Meanwhile, the macro mechanical properties are enhanced with the increase of the solid parameters (Poisson's ratio, elastic modulus), whereas they decrease with the increasing of the pore fractal dimension, and the varying curve can be obtained from the homogenization equations in this paper. The analytical solution in this paper can be utilized to predict the macroscopic mechanical properties of fractal porous media and to provide theoretical support for parameters selection of numerical simulation and scale upgrading.