Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities

The effect of surface energies, strains, and stresses on the size-dependent elastic state of embedded inhomogeneities are investigated. At nanolength scales, due to the increasing surface-to-volume ratio, surface effects become important and induce a size dependency in the otherwise size-independent classical elasticity solutions. In this letter, closed-form expressions are derived for the elastic state of eigenstrained spherical inhomogeneities with surface effects using a variational formulation. Our results indicate that surface elasticity can significantly alter the fundamental nature of stress state at nanometer length scales. Additional applications of our work on nanostructures such as quantum dots,…