Size effect on the effective bulk modulus of nanocomposites with core–shell nanospherical inclusions

Closed-form solutions are presented for the internal stress and effective bulk modulus of a nanocomposite by considering the effect of interface energy. The nanocomposite is made of three-phase structures: a nanospherical inclusion, a spherical shell on the surface of the spherical inclusion, and a macroscopically isotropic material. The results reveal the size-dependence of the effective bulk modulus of the nanocomposite. The elastic response of the nanocomposite depends on the interface energy and the characteristic dimensions of the nanospherical inclusion and spherical shell.