Effect of residual surface stress and surface elasticity on deformation of nanometer spherical inclusions in an elastic matrix

The analytical solution of the Eshelby problem, which describes the deformation of an elastic medium inside and outside a spherical inclusion with uniform internal eigenstrain and specified remote stress, is generalized taking into account both surface elasticity and residual surface stress. Expressions are derived for the internal and external Eshelby tensors and stress concentration tensors with regard to the above effects. A characteristic strain field inhomogeneity and its dependence on the inclusion diameter in the nanometer range (the scale effect) are found. It is shown that under certain conditions, the effect of residual surface stress surpasses that of surface elasticity.