  A consistent treatment of the coupling of surface energy and elasticity
within the multi-phase- field framework is presented. The model accurately
reproduces stress distribution in a number of analytically tractable, yet
non-trivial, cases including different types of spherical heterogeneities and a
thin plate suspending in a gas environment. It is then used to study the stress
distribution inside elastic bodies with non-spherical geometries, such as a
solid ellipsoid and a sintered structure. In these latter cases, it is shown
that the interplay between deformation and spatially variable surface curvature
leads to heterogeneous stress distribution across the specimen.
