Correlation of the electromagnetic and elastic properties of composities and microgeometries corresponding with effective medium approximations

Relationships between the effective conductivity and bulk and shear moduli of two‐component composites are presented and discussed. Some new identities amongst the geometric parameters which link together these effective properties are given. It turns out the effective medium approximation is consistent with all the new results. This is because the approximation is exact, after certain limits have been taken, for a family of hierarchical models which are described here.