Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress

The fundamental framework of micromechanical procedure is generalized to take into account the surface/interface stress effect at the nano-scale. This framework is applied to the derivation of the effective moduli of solids containing nano-inhomogeneities in conjunction with the composite spheres assemblage model, the Mori-Tanaka method and the generalized self-consistent method. Closed-form expressions are given for the bulk and shear moduli, which are shown to be functions of the interface properties and the size of the inhomogeneities. The dependence of the elastic moduli on the size of the inhomogeneities highlights the importance of the surface/interface in analysing the deformation of nano-scale structures. The present results are applicable to analysis of the properties of nano-composites and foam structures.