Size-dependent effective modulus of elastic composite materials: Spherical nanocavities at dilute concentrations

The effect of surface energy on the effective elastic properties was analyzed for elastic composite materials containing spherical nanocavities at dilute concentration. Closed-form solutions of the effective shear modulus and bulk modulus were obtained, which turn out to be a function of the surface energy and size of the nanocavity. The dependence of the elastic response on size of the nanocavity in composite materials is different from the classic results obtained in the linear elasticity theory, suggesting the importance of the surface energy of the nanocavity in analyzing the deformation of nanoscale structures.