Lower strain and stress bounds for elastic random composites consisting of two isotropic phases and exhibiting cubic symmetry

This work is concerned with a composite consisting of two linearly elastic isotropic phases which are distributed at the microscopic scale in such a way that the composite exhibits cubic symmetry at the macroscopic scale. Lower bounds on the second-order and higher order moments of the phase stress and strain fields of such a composite undergoing uniform macroscopic loading are provided in terms of the phase volume fractions and moduli. The lower bounds on the phase second-order strain and stress moments are proved to be optimal by showing that the stress and the strain fields inside appropriate finite-rank laminates achieve them.