Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds

TL;DR

This paper introduces a modified effective medium theory for elastic properties of composite materials, aligning it with electrical conductivity theory and enabling analysis across various percolation thresholds.

Contribution

A new elastic effective medium theory with variable percolation thresholds that improves modeling of inhomogeneous composites and aligns with cross-property relations.

Findings

Qualitative conclusions of the theory remain unchanged.

The theory allows broader class of composites with different percolation thresholds.

Conditions for elastic analogue of Dykhne formula are identified.

Abstract

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.