Bounds on the effective isotropic moduli of thin elastic composite plates

The main aim of this paper is to estimate the effective moduli of an isotropic elastic composite, analyzed within the framework of the Kirchhoff-Love theory of thin plates in bending. Results of calculations provide explicit functional correlations between the homogenized properties of a composite plate made of two isotropic materials, thus yielding more restrictive bounds on pairs of effective moduli than the classical (uncoupled) Hashin-Shtrikman-Walpole ones. Applying the static-geometric analogy of Lurie and Goldenveizer, enables rewriting of these new bounds in the two-dimensional elasticity (plane stress) setting, thus revealing a link to the formulae previously found by Gibiansky and Cherkaev. Consequently, simple cross-property estimates are proposed for the plate subject to the simultaneous bending and in-plane loads.