Numerical Investigation on Effective Elastic Modulus of Multifractal Porous Materials

The design of a novel material necessitates a fundamental understanding of its structure–property relation. Inorganic porous materials (media) such as natural soil and rock, and artificial ceramic and cement, exhibit multifractal characteristics in view of their structural heterogeneity. This paper presents a numerical investigation of the effective elastic modulus of multifractal porous materials. Two types of deterministic and stochastic cascading algorithms are employed to synthesize the multifractal fields, and then a mathematical formula is proposed to perform the conversion from the intensity of a multifractal field to the local elastic modulus of a multifractal porous material. Furthermore, a finite element method is used to achieve the homogenization of the local elastic modulus. Special attention is paid to the dependence of the effective elastic modulus on the structural heterogeneity of multifractal porous materials.