Analysis of the Behavior of Heterogeneous Media with Significantly Differing Physical Properties with Allowance for the Effective Dimension of the Space and Generalized Derivative Formalism

The effective coefficients of linear elasticity theory are obtained and analyzed with the aim to analytically describe heterogeneous media. This is done for an arbitrary dimension of the space under consideration and taking into account the generalized derivative formalism. The effective coefficients and their derivatives are explored for the presence of a carrier phase and a structural phase transition (percolation properties) over the entire range of volumetric concentration. Based on the analysis carried out, a comparison is made with the results of existing approaches and with the available data on colloids, suspensions, and granular media.