Abstract
We introduce new bounds and variational principles for the effective elasticity of anisotropic two-phase composites with imperfect bonding conditions between phases. The monotonicity of the bounds in the geometric parameters is used to predict new size effect phenomena for monodisperse and polydisperse suspensions of spheres. For isotropic elastic spheres in a more compliant isotropic matrix we exhibit critical radii for which the stress state, external to the spheres, is unaffected by their presence. Physically all size effects presented here are due to the increase in surface to volume ratio, as the sizes of the inclusions decrease. The scale at which these effects occur is determined by the parameters [Formula: see text] and [Formula: see text]. These parameters measure the relative importance of interfacial compliance and phase compliance mismatch.
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