  It is discussed that the classical effective medium theory for the elastic
properties of random heterogeneous materials is not congruous with the
effective medium theory for the electrical conductivity. In particular, when
describing the elastic and electro-conductive properties of a strongly
inhomogeneous two-phase composite material, the steep rise of effective
parameters occurs at different concentrations. To achieve the logical
concordance between the cross-property relations, a modification of the
effective medium theory of the elastic properties is introduced. It is shown
that the qualitative conclusions of the theory do not change, while a
possibility of describing a broader class of composite materials with various
percolation thresholds arises. It is determined under what conditions there is
an elastic analogue of the Dykhne formula (for the effective conductivity). The
introduction of the theory with the variable percolation threshold paves the
way for describing the magneto-elastic properties of magnetorheological
elastomers, as it has been achieved for magneto-dielectric and magnetic
properties recently.
