Prediction of Elastic Moduli of Porous Materials with Equivalent Inclusion Method

Abstract

This study presents a methodology to predict the effective elastic moduli of porous materials with respect to the variation of the void volume fraction and the void aspect ratio. The Mori-Tanaka theory is also applied to determine the overall stress-strain relation of inclusions embedded in a matrix, regardless of whether the matrix is isotropic, cubic, or transversely isotropic material. Our analysis results indicate that the overall elastic moduli of a composite are a function of a matrix's elastic moduli, inclusion elastic moduli, inclusion Eshelby tensor (depending on the aspect ratio of the inclusion), and inclusion volume fraction. In addition, the equivalent inclusion method is employed to model the voids of porous materials as inclusions in which the elastic moduli are nulls. Analysis results with foamed aluminum as demonstration of the effectiveness of the proposed methodology indicate that the longitudinal elastic modulus El 1, shear moduli G₁₂ and G₁₃, and Poisson's ratio vl₂ appear to increase with the increment of the void aspect ratio. Meanwhile, the transverse elastic moduli E₂₂ and E₃₃, out-plane shear modulus G₂₃, and Poisson's ratio v ₂₁ as well as V₂₃ decrease with an increasing aspect ratio of the void. The good correlation of the numerical results in longitudinal elastic modulus El I and bulk modulus Kwith experimental data verifies that the methodology proposed herein is highly accurate.