An analytical solution of Eshelby problem, describing the deformation of en elastic medium containing an inclusion having different elastic constants due to uniform remote stress field, uniform eigenstrains within the inclusion and uniform surface eigenstrains, was obtained for a spherical inclusion. It was shown that, while considering inhomogeneous media with eigenstrains, the assumption that the interfaces possesses some specific properties leads to the necessity to account both for effect of residual surface stress (or surface eigenstrain) and surface elasticity simultaneously. The problem of determining the stressed-strained state for a described configuration was formulated and solved in terms of small deformations. Expressions are derived for both internal and external Eshelby tensors and for stress concentration tensors with regards to both effects. It is shown that due to the considered surface effects the stresses and strains become inhomogeneous within the inclusion. It is shown that under certain conditions the effect of residual surface stress may surpass that of surface elasticity. In case of a vanishing residual stress, the obtained results reduce to the solution.
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