Model of homogenisation for analysing the effect of micrometre pore sizes on the elastic moduli of porous materials

A homogenisation model for analysing the effect of micrometre pore sizes on the engineering moduli of elasticity of porous materials was proposed. In the proposed model, the engineering coefficients of localization of total strains (LTS coefficients) are considered instead of the classical strain localization tensors. For a pore, these coefficients represent the ratio of the sum of the strains in the volume of the pore to the sum of the strains in the volume of the porous body. To estimate the elastic moduli of a material with an arbitrary pore size, it is sufficient to have information about the elastic moduli and the LTS coefficient of a material with one basic pore size. Then, in Eshelby’s model of equivalent inclusion, a transition to LTS coefficient for material with arbitrary pore size is achieved, and its elasticity moduli are determined. The results for Young’s modulus of porous titanium, with different sizes of spherical pores, completely conform with the experimental data. We have obtained a model theoretic estimate of the upper bounds of Young’s modulus of porous materials with infinitely small pore size. For the spherical pores, the proposed assessment coincides with the upper limits of the Hashin–Shtrikman bounds.