‘Perfectly disordered’ medium as a model for the description of micro-inhomogeneous mixtures

Abstract

The correct description of the macroscopic (overall) physical properties of micro-inhomogeneous (composite) materials by micro-mechanics methods (the self-consistent schemes, for example) requires information about the microstructure and texture of such materials. Often, such information (of shapes inhomogeneities and peculiarities of their spatial distribution) is not available. In this paper, we suggest a method of calculation of the characteristics of micro-inhomogeneous materials that could be applied to a wide class of isotropic materials. This method assumes the absence of a closed order in the material microstructure (a ‘perfectly disordered’ (PD) medium). We used the PD approximation to predict the effective thermo- and poroelastic, electric and thermal properties of micro-inhomogeneous media.The expressions for the effective characteristics obtained by this method are always inside of the Hashin–Shtrikman universal bounds. For a two-phase material with fluid component, the effective bulk module satisfies Gassmann's relation for fluid-filled porous media and generalizes such a relation to inhomogeneous thermoelastic and poroelastic media. A comparison of the theoretical results with available experimental data shows a satisfactory coincidence even in the case of high contrast of the component properties.The simplicity of the numerical realization of the method makes it attractive for applications in the absence of detailed information about the material's microstructure.